Explorez tous les épisodes du podcast プレプリどんどん: math.NT

arXiv math.NTの新着論文38本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-16/

1. The Waring-Goldbach problem in short intervals under the Generalized Riemann Hypothesis
2. Mean Lindel\"of Hypothesis and Prime Geodesic Theorem on Bianchi Manifolds
3. A formula for the rank over $\mathbb{Q}(t)$ of the elliptic curve $y^2=x^3+At^6+Bt^3+C$
4. Number fields as curves over $\mathbf{F}_1$
5. Simultaneously small continued fraction entropy and base $b$ entropy
6. Elementary proofs of congruences modulo 5 for overpartitions with restricted odd differences
7. Rational Points near Monofractal Curves and the Strong Oscillation Principle
8. Local Langlands functoriality for Yu's supercuspidals I: Kaletha's parametrization
9. Local Langlands functoriality for Yu's supercuspidals II: Fargues--Scholze's parametrization
10. Twisted Rational Zeros and Local-Global Principles for Linear Recurrence Sequences
11. Higher Schwarzians of Elliptic Double Covers and Eisenstein--Kronecker Functions
12. The Furstenberg-S\'ark\"ozy theorem for sums of an even number of odd powers
13. An infinite family of imaginary biquadratic fields with a large class number
14. Laurent series expansions for the Barnes multiple zeta function
15. Triple divisor type functions in arithmetic progressions to prime power moduli
16. Iwasawa theory of (directe) Cayley graphs
17. The Local Ghost Theorem in the Tr\`es Ramifi\'e Case
18. Distribution of squarefree integers with double congruence conditions
19. Prime-power congruences for level-one eigenforms
20. Extreme values of quadratic Hecke $L$-functions
21. On $t$-sumfree sequences
22. Mixed moment of $GL(2)$ and $GL(3)$ $L$-functions in the level aspect
23. An additive problem in connection with some quadratic real fields with class number one
24. Powers of the Thue--Morse Series: 2-Adic Valuations and Automatic Odd Parts
25. Refined conjectures on Fitting ideals of BDP Selmer groups
26. Modular functoriality for finite groups
27. Uniform Mordell-Lang conjecture for semiabelian varieties
28. A class formula for effective Anderson motives
29. On Sarnak--Str\"{o}mbergsson conjecture
30. Improved bounds for Szpiro's conjecture
31. Even-degree Hermitian Ikeda lifts via Fourier-Jacobi descent
32. Hypothetical connection of the theta functions of Dirichlet characters with the real cyclotomic fields
33. Loop spaces, twistor $\mathbb P^1$ and tempiric parameters
34. List Decoding, Linear Hashing, and Furstenberg over $\mathbb{F}_q$
35. Block-count constrained harmonic sums: spectral expansion and block-directed Euler-Maclaurin
36. On a classical zero-sum invariant II: Disproof of a long-standing conjecture
37. Small degree isogenies between conjugate principally polarized superspecial abelian surfaces
38. A perimeter analogue of Franklin's identity and an inequality related to the parity of parts

arXiv math.NTの新着論文69本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-15/

1. The Strong 24-Conjecture
2. Theta functions after Weil
3. Dynamical uniform boundedness for unicritical polynomials and elliptic curves of large rank
4. Arithmetic Siegel-Weil for the spherical Hecke algebra
5. Galois representations and modularity for twisted moments of Kloosterman sums
6. Pointwise ergodic theorems along sequences of intermediate growth
7. Spherical statistics and phase transitions in high-dimensional lattices
8. Finiteness of an Isogeny Class via Equidistribution
9. Prime and Nonprime Totatives: A Sharp Construction and Exact Thresholds
10. The optimal scale in Linnik's microsquare problem for almost all integers
11. Generalized Wieferich primes and monogenic polynomials
12. Density of Vanishing of Certain Eigenspaces of Cyclotomic Class Groups
13. A Local Proof of Langlands's Second Main Lemma for Local Epsilon Factors over Nonarchimedean Local Fields
14. Modular and Shimura curves $X_0^D(N)$ embedded in $\mathbb P^1 \times \mathbb P^1$
15. Reduction of integer tiles via CRT and base-p digits
16. Patterns in the Markov numbers and their generalizations
17. Quantitative linear independence for square roots
18. Twisted Lubin-Tate Big Witt Vectors and Fleck-Sun-Wan Congruences
19. On Decomposition of Drinfeld cusp forms of level $t$
20. Golden-ratio growth of Conway's subprime closure
21. Two-Height Approximation and Mahler's Problem on Liouville Numbers
22. A Central Limit Theorem for Coprime Pair Counts in Randomly Translated Disks
23. Surjectivity of Finite Rank-Capped Enots-Wolley Sequences
24. The Jensen--P\'{o}lya program and inequalities for arithmetic sequences
25. Cubic AGM graphs and Hessian $3$-isogenies over finite fields $\mathbb{F}_q$ of odd characteristic with $q \equiv 2 \pmod3$
26. Character sums on an oriented singer conic and explicit Ramanujan double covers
27. An explicit power-saving bound for S\'{a}rk\"{o}zy's Theorem on shifted primes, assuming GRH
28. Bloch cycles and the weak two-variable Chinburg conjecture
29. Dynamical generalizations of Chowla's conjecture on short averages
30. Elimination of Ren\'e Peschmann's 968 Remaining Hard Fibers for the Perfect Cuboid Problem
31. Asymptotic Formula for Biregular Overpartitions
32. Critical Restricted Sumsets at the Boundary $\lvert A\rvert+\lvert B\rvert=p$
33. Prime Plus a Non-Square-Free Integer: An Elementary Approach
34. Transcendence of Montgomery Reduction Factor in the Ring of Integers Modulo Infinitely Large Primes
35. A proof of Sylvester's conjecture
36. The typical size of Hecke eigenvalue sums is $o(\sqrt{x})$
37. Two-term dilogarithms, mixed-base Nahm sums, and Fricke symmetry
38. Ekedahl-Oort strata meeting the supersingular locus
39. Laurent coefficients of Zagier-type zeta function {\`a} la Ishibashi and arithmetic aspects of extended Ramanujan period function
40. The Dynamical Mordell--Lang Conjecture for Relatively \'{E}tale Systems over Products of Curves
41. On the largest prime factors less than $y$ of consecutive shifted primes
42. Algorithms for $p$-rationality and for $p$-saturation of units
43. Algebraic independence of the exponential and Weierstrass $\wp$-functions
44. On the arithmetic of Tate-Shafarevich groups via Kolyvagin's conjecture
45. Optimising Selberg's method for critical zeros
46. On the number of solutions to $S$-unit equations
47. Hecke structure of quaternionic modular forms mod $p$
48. Periodicity and Period-Length Bounds for Browkin $p$-Adic Continued Fractions
49. An extension of algebraic independence of special values for non-lacunary power series
50. Long runs of integers with small prime factors and the divisor function of $n!$
51. A Construction of an Extremal Even Unimodular Lattice of Rank $88$
52. Singular automorphic products and BKM algebras
53. A septic covariant and the Hermite--Joubert problem in degree seven
54. Another proof of the $U^4(\mathbf{F}_p^n)$-inverse theorem
55. Cauchy laws for zeta logarithmic derivatives and stationary Stieltjes transforms
56. Low moments of Hecke eigenvalue sums
57. A lattice family with kissing constant $\tau(\mathcal{L}_n) \ge e^{\sqrt{n}}$
58. Zeros in The Character Table of The Wreath Product of The Symmetric Group
59. Matrices over non-commutative rings as sums of fifth and seventh powers
60. Subset-Sum Density Realization in Locally Finite Abelian Groups
61. Torsion, Betti rank, and small points in semiabelian schemes
62. Thresholds and Fluctuations for Colorful Arithmetic Progressions in Sparse Random Colorings
63. Noether's problem for $A_6$ and $A_7$
64. Growth beyond exponent $3/2$ for convexity and iterated sum sets
65. AKE principles in roughly deeply ramified henselian valued fields
66. Algebraic Structures on Sets of Partitions
67. NP-hardness of ideal lattice problems
68. Geometric realizations of Brauer classes on K3 surfaces from hyperk\"ahler contractions
69. Dynamical Mordell--Lang Conjecture for Higher-Rank Radially Ramified Skew Products

arXiv math.NTの新着論文25本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-14/

1. An adelic approach to the Kudla-Millson lifts over totally real number fields
2. Local-global principles for visibility of lattice points on parameterized curves
3. On the variation of slopes over moduli stacks of Galois representations
4. Critical convergence and Hausdorff measures for generalized Flint Hills series
5. $S_h$-sets in abelian groups
6. A Generalization of S\'ark\"ozy's theorem in function fields
7. Zeros of Quasimodular Forms Defined by Iterated Sums
8. The first moment of quadratic Dirichlet $L$-functions in the even hyperelliptic ensemble
9. Tight universality of $m$-gonal forms with minimal criterion sets
10. Gauss Genus Theory in Characteristic 2
11. Projective Kernels and Replicability in Modular Function Theory
12. Classification of torsion of elliptic curves over quintic fields
13. Large fluctuations of extended Rademacher random multiplicative functions
14. Projection and fibering in groups of bounded exponent
15. Kronecker sequences beyond the torus: nearest-neighbour distances and best returns
16. Iwasawa theory of CM elliptic curves at potentially supersingular primes
17. Kolyvagin's conjecture at non-ordinary primes
18. An asymptotic formula for a cubic moment of $GL_2$ $L$-functions
19. Jacquet--Rallis transfer for GL(2)
20. Quasipolynomial density bounds for $K$-point configurations in $\mathbb{Z}^d$
21. Eta-Quotient Representations for a Three Parameter Family of Modular Functions Associated with the Rogers-Ramanujan Continued Fraction
22. Serre's problem on statistics of Brauer symbols
23. Poincar\'e duality for pro-\'etale $\mathbf{Q}_p$-local systems
24. Characteristic Classes of Adelic Vector Bundles and Applications
25. Non-archimedean Monge-Amp\`ere measures for toric metrics on subvarieties of toric varieties

arXiv math.NTの新着論文26本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-11/

1. A New Sparse Algorithm for Polynomial GCD over Integers
2. Sums of distinct divisors of factorials
3. Ordinary 3-Isogeny Graphs and Improvement of Supersingularity Testing for Twisted Hessian Curves over Prime Fields
4. Effective estimates for exponential sums with multiplicative coefficients
5. Rational Approximations for Reciprocals of Multiple Zeta Values and Trivariate Cauchy Numbers
6. A $p$-adic monodromy theorem for curves
7. Moments and Non-Vanishing of Maass Form Symmetric Square L-Functions in Short Intervals
8. Log-crystalline representations and $(\varphi, \Gamma)$-modules
9. The irrationality measure of {\pi} is at most 7.101862832357
10. On the bounded-conductor finiteness conjecture in equal characteristic
11. Sharp unconditional moment bounds for products of L-functions
12. Internal congruences modulo powers of $2$ for overpartition tuples with odd parts
13. Generalized Frobenius Partitions Modulo Powers of $2$
14. Bounded asymptotic bases for linear forms
15. Chowla's non-vanishing conjecture over $\mathbb{F}_q(T)$
16. The asymptotic in Waring's problem over function fields beyond twice the degree
17. On the Mahler measure and root distribution of the $Q$-polynomial of links
18. The 2-Adic Valuation of the Order of the All-Ones Class in the Sandpile Group of a Square
19. F-theory on K3 surfaces and orthogonal modular forms
20. A dynamic point of view on universality for random matrices over finite local rings
21. Quantitative universality for products of i.i.d. random matrices
22. Rankin--Selberg integrals of opposite conductor--one newforms
23. Divisibility and torsion in higher Chow groups over arithmetic fields
24. Reversibility and its asymptotic counting in Picard group
25. A maximal function field of genus $17$ over $\mathbb{F}_{11^2}$
26. Cusp restrictions and Bunke--Naumann invariants with level structure

arXiv math.NTの新着論文33本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-10/

1. A proof of Hare's $\epsilon$ unfair conjecture
2. The density of long runs of non-$r$-free integers
3. Spectral Algebras of Abelian Cayley Graphs
4. Triple intersections for algebraic curves on the real torus
5. Cyclotomy of symmetric polynomials
6. Effective Euler Sums
7. The addition on totally positive integers uniquely determines the totally real number field
8. Generic Manin-Mumford
9. Regular Arithmetic Functions, Volume I. Theory, Applications, Examples
10. What Does MMLU Actually Measure? A Psychometric Audit of Difficulty Structure in Aggregate Benchmark Scores
11. Models of Elliptic Curves with Maximal 2-adic Image Subject to a Rational 2-Isogeny
12. Integer group determinants for the elementary abelian group of order 49
13. The three Kanade-Russell identities modulo nine
14. From Pythagorean Runs to Pell-Generated Cubic Runs
15. An elementary approach to Sun Kim's general theta function identities
16. Universal norms and de Rham representations
17. Unramified Motivic Alternating Multiple Mixed Values
18. Non-vanishing of symmetric square $L$-functions in the weight aspect
19. Pencils of norm form equations and a conjecture of Thomas, II
20. Diophantine approximation with primes in an arithmetic progression
21. A Counterexample to a Conjecture of Liu and Qian and a Refined Inverse Theorem for Restricted Sumsets in $\mathbb{Z}_p$
22. Inertial multiplicity bounds for two dimensional projective representations and bounds for the number of $\operatorname{PSL}_2(\mathbb{F}_q)$ and $\operatorname{PGL}_2(\mathbb{F}_q)$ number fields
23. Faltings' Isogeny Theorem via Equidistribution
24. Quasi-modularity of symmetric quasi-shuffles
25. Sharp local estimates for smooth numbers
26. On the syntomic regulator of the Hesse cubic curves and $p$-adic hypergeometric functions
27. Integer group determinants for abelian groups of order 24
28. On the Number of Hecke Eigenvalues of Same Sign on $\mathrm{GL}_n$
29. Irreducibility of truncations of the Catalan generating function
30. $B_h$-sets and perturbations in normed vector spaces
31. The algebraic geometry of 3-by-3 magic squares of squares
32. Positivity and Asymptotics for Chenevier's Orthogonal Polynomials
33. Distinguished standard modules for $\mathrm{GL}_{2m}(\mathbb{C})/\mathrm{GL}_m(\mathbb{H})$

arXiv math.NTの新着論文81本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-09/

1. Lower bounds for some value sets over finite fields: incidence geometry and Bourgain's group expansion theorem
2. On the Diophantine Equations Arising from Three-Term $b$-Concatenations in Pell-Type Sequences
3. Primes with Restricted-Digit Differences
4. On the classification of small cyclotomic integers
5. On the class number of certain cyclotomic fields
6. A $q$-microscope for mock-theta denominator patterns
7. Infinite-order $p$-adic differential equations for Hurwitz-type Euler zeta functions: Higher-dimensional extensions and uniqueness of bounded solutions
8. The entropy of coclass one and of SmallGroup(729,45)
9. Central non-vanishing of Dirichlet $L$-functions
10. From dimension four to dimension five in the Tate conjecture for abelian varieties over finite fields
11. Lattice point visibility along polynomials has density one
12. Normal Behavior and Periodic Points of a Pseudo-Aliquot Map Associated with the Dedekind Psi Function
13. Mean Values and Normal Order of a Successive-Iterate Ratio of Dedekind's Arithmetic Function
14. Bounds on Whittaker Functions for $\mathrm{GL}(n)$
15. Fields of definition of $p$-torsion points of elliptic curves and their ramification
16. Methods to Find Integer Points on the Elliptic Curve of Factorizable Polynomial Equation
17. Optimization of Quadratic Sieve Algorithm Implementation for Large Integer Factorization
18. Unsupported Cyclotomic Divisors in Three-Prime Integer Tilings
19. Generalized Zeckendorf expansions of the 2nd order
20. A Fricke transformation for cubic-residue eta products of level 13
21. High dimensional Riemann--Roch spaces in linear spaces with small squares
22. Three Irrationality Results for the Dilogarithm: Rhin--Viola and Viola--Zudilin Constructions at $-1/4$, $1/5$, and $-1/3$
23. Maximising the number of solutions to linear equations
24. $p$-adic properties of division polynomials and algebraic sigma functions
25. Upper bounds for arithmetic functions over polynomial values via Chebotarev--Sato--Tate distributions
26. The method of telescoping continued fractions
27. Counting Representations of Quadratic Forms
28. A Proof of Bala's Congruence Conjectures for A158690
29. Parameterized partial theta identities and a unified $q$-difference proof
30. The Normal Form of Smith's Matrices
31. On a problem of Nathanson related to minimal asymptotic bases and maximal asymptotic nonbases
32. Prime pairs along rays of prime indices
33. On Dynamical Mordell-Lang Conjecture for Split Map
34. Asymptotically optimal packings of arithmetic progressions with prime differences
35. $\vec M$ Versions of Andrews-Gordon Identities Revisited
36. Zeros of Ramanujan-Like Polynomials
37. Residual finiteness and cuspidal cohomology of Picard modular surfaces
38. Sharp Diameter Bounds for Nonnegative Cyclotomic Multiples
39. A pencil of quadratic forms in nine variables with no member of Witt index four
40. The spectrum of $(\xi\alpha^n)$ can be uncountable
41. Equidistribution of small points over finitely generated fields
42. The Artin-Hasse $p$-section: weighted convolutions and $p$-adic recovery
43. Simple critical zeros and distinct zeros of the Riemann zeta-function in short intervals
44. The Fibonacci numbers are not an additive uniqueness set for multiplicative functions
45. Relative $(\varphi, \Gamma)$-modules and $p$-adic differential equations
46. A Lang-Trotter Problem for Non-Geometric Quadratic Inductions
47. Replication Descent and $J$-Finality of Replicable Functions
48. Todd's relation conjecture and binary relations for multiple zeta values in positive characteristic
49. Pascal tiling and congruences modulo N in Pascal's triangle
50. Moments of the Crank Statistic for $t$-Core Partitions and Overpartitions
51. Prescribed Abscissae on Congruent-Number Curves over Simplest Cubic Fields
52. Second derivatives of $p$-adic $L$-functions and the Shafarevich--Tate group of rank-two CM elliptic curves
53. Counting Survivor Sets: Exponential Equivalence with Prime-Admissible Sets
54. Symmetric power L-functions of a weighted hyper-Kloosterman family
55. A geometric Jacquet--Langlands correspondence for Shimura varieties
56. Four explicit continued fractions for values of the Lerch transcendent and the Hurwitz zeta function
57. A Problem on the largest divisor $d$ of $N$ with $d\leq \sqrt{N}$
58. Reduction Modulo Binary Polynomials with Logarithmic Feedback Depth
59. On a problem of Erd\H{o}s and Nathanson related to minimal asymptotic bases of order $h$
60. On the cardinality of the exception set in Littlewood's discrete conjecture
61. Generalizing a Pair of Diophantine Equations
62. The modulo 9 Kanade--Russell identities and their Nahm-sum duals
63. Rational functions over finite fields with Galois closure of genus zero
64. Sharp order-preserving integer models for short additive equalities
65. The Archimedean place is a blurred interval at infinity
66. Coarse moduli of motivic augmentations
67. Partial Results on Hankel Determinants and the Corresponding J-Fractions of a Sequence Related to Bernoulli Numbers
68. Polynomial point counts for moduli spaces of curves with marked points
69. The Constant in Thomae-Type Formulas for Eight Points on the Complex Projective Line
70. Microlocalization and singular supports of constructible \'etale sheaves
71. A Uniform Product-Difference Theorem for Dense Subsets of $\mathbb Z^2$
72. External Difference Families Arising from Two or Three Cyclotomic Classes
73. The exponent of harmonic LCM avoidance
74. Solutions to 6 problems in recurrence and Van der Corput sets
75. Logarithmic $A_{\mathrm{inf}}$-cohomology, Part II
76. Proofs of Some Kanade--Russell Mod 12 Conjectures
77. Majorization and additive tuples in $\mathbb{Z}_2^n$
78. A Perfectoid Pro-\'Etale Lie Torsor Can Have a Non-Surjective Sen Map
79. On the $a$-number of Fermat type function fields and some of their subfields
80. The range and omitted values of a certain sequence involving the partition function
81. The sharp constant in the Mashreghi-Ransford inequality

arXiv math.NTの新着論文23本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-07/

1. Multiple zeta values in $\lambda$-rings
2. SIC dimension towers via cyclotomic polynomials
3. A counterexample to the Chung-Graham-Spiro gap-set conjecture
4. Hilbert's Irreducibility for $\mathbb{G}_m$
5. Degeneration of monodromy in the theory of Eisenstein congruences for classical groups
6. Numerical experiments on the Hardy conjecture for the Gauss circle problem
7. On multiply induced characters
8. On the Divisibility Relation $\sigma(n)\mid\sigma(n+h)$ and a Generalized Erd\H{o}s--Sierpi\'nski Conjecture
9. Distribution properties of generalized polynomials
10. The Right Edge of the Zero Set of the Fibonacci Zeta Function
11. Lattice point visibility along powers of quadratic polynomials
12. The Prouhet--Tarry--Escott problem for subsets with small doubling in integral domains
13. Counting level-raising congruences using modular representation theory
14. Local Jacquet-Shalika integrals and modifying factors
15. Proof of a Conjecture of Cui, Gu and Tang on 18-Colored Generalized Frobenius Partitions
16. F-sets of arbitrary finite width
17. Distribution of points near the origin in the $d$-dimensional Lagrange spectrum
18. Short arithmetic terms express the cardinality of elliptic curves in Weierstra{\ss} normal form over finite fields
19. Cone upgrade for effective equidistribution and weighted Khintchine--Schmidt theorem on fractals
20. Coleman Isomorphisms in Syntomic Cohomology and $\mathrm{THH}$
21. A Log-Free $n^{1/5}$ Bound for Chowla's Cosine Problem
22. Arithmetic Polyhedra
23. Counting sets with given doubling via dimension

arXiv math.NTの新着論文29本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-04/

1. An upper bound for an exceptional automorphism group
2. Perfect numbers, Wieferich primes and the solutions of $\binom{2n}{n}\equiv 2^n \bmod n$
3. Poissonian pair correlations for the three-particle Sutherland model
4. Skolem-Mahler-Lech in rings of positive characteristic: a shorter proof and a multi-dimensional generalization
5. Factorization patterns and fields of definition of $\ell$-torsion points on the Jacobians of genus 3 hyperelliptic curves
6. On lifting representations and actions on curves of the metacyclic groups $C_{p^s}\rtimes C_m$
7. Representation Defects and Cassels Pairings for Congruent Number Curves
8. Resolving a conjecture on permutation polynomials over $\mathbb{F}_{2^n}$
9. Odd denominators in the Lonely Runner spectrum for six speeds
10. Prime-power Diophantine tuples
11. The Klein-V\'elu septic, 2-Division, and modular function fields of level 14
12. The derived set of multiple star polylogarithms
13. The $\mathfrak{sl}_2$-algebra structure of multiple Eisenstein series
14. Supersingular Elliptic Curves Without Inseparable Small Degree Endomorphisms
15. Overcolored Partition $k$-tuples Restricted by Parity of the Parts
16. Arithmetic probability measures
17. The groups $\operatorname{SL}_2(\mathbb{F}_{13})$ and $\operatorname{SL}_2(\mathbb{F}_{19})$ are Galois over $\mathbb{Q}$
18. Galois representations ramified at one prime via relative deformation theory
19. On the exponential sum over squarefree integers
20. Short character sums of inhomogeneous polynomials
21. The subconvexity problem for symmetric square $L$-functions in level aspect
22. Catalan's constant is irrational
23. Some generalizations of Oort's conjecture
24. Connections between colored restricted $b$-ary and ordinary partitions
25. Extension Problems for the Vladimirov--Taibleson Operator and the Hierarchical Laplacian
26. From Ordered Bernoulli Levels to Critical-Line Geometry: Integer Quantization, Bernoulli Residual Phase, and Prime-Power Spectra
27. A Fej\'er--Riesz inequality for Dirichlet series
28. The Prime Clockwork: A Dynamic Representation of Modular and Multiplicative Arithmetic
29. Oort's conjecture for split unitary Shimura varieties

arXiv math.NTの新着論文27本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-03/

1. A lower bound for the Call-Silverman height in cyclotomic extensions
2. On the cuspidal cohomology of Iwahori congruence subgroups of $\mathrm{SL}(3, \mathbb{Z})$
3. Ranks and integer points on elliptic curves induced by Fibonacci triples
4. On everywhere locally soluble varieties in families over toric bases
5. When Fibonacci and Lucas Meet Smith: A Computational Exploration
6. Jacquet-Zagier treatment of the beyond endoscopy trace formula for $\mathrm{GL}_2$
7. Summing the reciprocal of the polynomial appearing in Fermat's Last Theorem
8. Bounding Selmer Groups of Superelliptic Jacobians via Class Groups
9. Affine Copies of Three-Point Patterns in Sets of Integers
10. On the counting function of square-full numbers
11. Regularised double shuffle relations for planar Arborified Zeta Values
12. On the Growth of Denominators of Simultaneous Best Diophantine Approximations in the Euclidean Norm
13. Large values of cubic and quartic Dirichlet $L$-functions of prime moduli
14. A Two-Variable Zeta Function for a Parity-Perturbed Hofstadter Q-Recursion: The Exceptional t = -1 Slice and Gaussian Boundary Layers
15. The Hasse norm principle for $A_4$-quartic extensions of global function fields
16. Improved Weyl bounds on short intervals
17. On the occurrence of congruence multiplicities between Ramanujan's theta functions
18. On divergence related to Riemann--von Mangoldt's explicit formula of the prime-counting function
19. Adelic points and unmramified Brauer approximation for classifying stacks
20. Petersson-Rigid Lattices in a Census of 100 Rank-Three Root Bases
21. A new proof that more than $2/3$ of the zeros of the Riemann zeta function are simple and on the critical line
22. Iterated-sumset spectra: The complete exponent law and its rank geometry
23. Sparse $k$-AP Covering Sets and the Arithmetic Kakeya Conjecture
24. $\mathfrak{sl}_2$-action on the uri Lie algebra
25. A finiteness theorem for geodesic Leech wheels
26. Fourteen lonely runners
27. Finite extensions of abelian schemes and duality for commutative group stacks

arXiv math.NTの新着論文32本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-02/

1. Reducing Every Set of 36 Consecutive Integers to Zero by Differences of Squares
2. Colombo's Determinant Problem
3. The shortest harmonic sums with decreasing denominator
4. From Common-Slot Chains to Heisenberg Central Products over Global Fields
5. Smooth Diffeomorphisms and Mahler's Problem on Liouville Numbers
6. Almost $k$-th powers in short intervals
7. Exceptional points on Atkin--Lehner quotients
8. Explicit Exponential Sum Estimates and Approximate Functional Equations for the Zeta Function
9. Distribution of Kaneko's val function
10. A unification of Euler-Maclaurin and Euler-Boole summation formulas
11. Improved bounds in Birch's theorem for forms in many variables
12. Universal murmuration and Hecke augmentation
13. Covering Projective Height Balls by Subspaces in Rigid Adelic Spaces
14. Sharp lower bounds for shifted moments of Dedekind zeta functions
15. Nonabelian Chabauty for the Thrice-punctured Line over Cyclotomic Fields
16. An improvement on the largest prime factor of $n^2+1$
17. New classes of trace-form permutation polynomials and their compositional inverses
18. Regularized spectral expansion of a Rankin--Selberg period and moments
19. Confluence relations for $q$-analogues of multiple zeta values
20. A General Construction of Codes from Drinfeld Modules
21. On the Ramification of Quadratic Fields where there is a torsion growth
22. A Proof of Fraenkel's Conjecture
23. Ten unknowns for Hilbert's tenth problem over the integers
24. The First Two Exceptional Boundaries for Sets with Few Subset Sums
25. Shifted poles and chamber cancellation for classical Witten zeta functions
26. Infinite transitivity of tame groups of automorphisms of affine spaces
27. Hodge--Tate splitting and Akizuki--Nakano vanishing in positive characteristic
28. Deciding superellipticity and computing the Weierstrass normal form
29. Two-photon quantum Rabi models - Spectral degeneracy and symmetries
30. On Algebraic Integrability of Vector Fields with Rational Function Coefficients that Separate Variables
31. Sharp Threshold for Universality of Rational Canonical Forms over a Finite Field
32. $A_1$ - Coulomb branches over finite fields and Selberg Character sums

arXiv math.NTの新着論文48本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-01/

1. On weighted forms in many variables
2. Stable Solutions to Generalizations of Fibonacci Relations of Higher Order
3. $q$-Analogues of some supercongruences related to generalized Van Hamme-type supercongruences
4. Counterexamples to O'Neil's Period-Index Problem on Elliptic Curves
5. Vanishing of $\mathrm{Sha}(A/K)[\mathfrak{P}^\infty]$ and its consequences for the anticyclotomic Iwasawa theory of $\mathrm{GL}_2$-abelian varieties
6. The average number of rational preperiodic points of polynomials over $\mathbb{Q}$
7. Analogue of Cardy's formula on the 60-degree parallelogram: a modular approach
8. The Shimura Lift and Hilbert Modular Forms
9. Kato's main conjecture for nonordinary modular forms
10. Lagrange spectrum for Diophantine approximations of complex numbers with real part equal to one half
11. Luo's Spectral Large Sieve Inequality on Short Intervals
12. Bloch-regulator Principal Parts of Cyclotomic Iwasawa Pseudomeasures
13. On the special values of Berndt's generalized $L$-function
14. Counting integral points near a curve in the n-dimensional Euclidean space
15. Wallis-type products with polynomial exponents and the Dirichlet beta function at negative integers
16. Exact logarithmic Hausdorff and capacity exponents of the non-Brjuno set
17. Difference of the modular function $\omega_{2}(\tau)$, revisited
18. Euler Characteristics of $\mathrm{SL}_4(\mathbb{Z})$ and $\mathrm{GL}_4(\mathbb{Z})$, and their cohomological consequences
19. On supersingular isogeny graphs of Drinfeld modules
20. The arithmetic of critical values II: critical elliptic curves
21. Hecke Subalgebras and Local Newforms for the Metaplectic Double Cover of $\SL_2(\mathbb Q_p)$
22. Average twin prime conjecture for elliptic curves in arithmetic progressions
23. $D(N)$-quadruples in upper-triangular $2\times2$ integer matrices
24. Lower Bounds for Moments of $L$-functions
25. Matrix representations and arithmetic properties of jacobsthal numbers via binary 3x3 matrices
26. Sets whose differences avoid a bracket quadratic
27. Complete characterization of a class of complete permutation quadrinomials over \(\mathbb{F}_{q^2}\)
28. $13$ unknowns over quadratic integer rings and Lucas congruences
29. Relative Langlands duality of the Bump-Friedberg-Ginzburg $\mathrm{GSO}_6$-integral
30. Joint Equidistribution of Subspaces of Bounded Height in Rigid Adelic Spaces
31. Unit Indices of Prime-Index Shanks Orders
32. Density of the multidimensional Lagrange spectrum
33. An Explicit Belyi Map for the Wiman Sextic and Cusp Forms for a Noncongruence Subgroup
34. Reduced polynomial lifts of APN permutations over Galois rings and effective non-APN bounds
35. Normal and Lognormal Asymptotics for Lattice-Point Counts in Random Translates of High-Dimensional Balls
36. Counting solutions to quadratic forms in eight prime variables of off-diagonal rank $3$
37. Subconvexity of Short $k$-Free Exponential Sums in $\mathbb{F}_q[t]$
38. Large zeta sums and zeros of the Riemann zeta function
39. Bounded gaps between primes
40. Quantitative time-averaged spherical means along equidistributed spirals: Diophantine rates and limits of uniformity
41. Lattice Green's function of the hyperkagome lattice: modular uniformization at level 30 from an orthogonal differential Galois group
42. Flat connections on moduli spaces I: Local (1,0)-extension of the DHS connection
43. Generalized Jantzen filtration, hyperbolic restriction, and characteristic cycles
44. Pseudo-spherical representations and types for covers of split tori
45. On the Babylonian Division of Trapezoids
46. Recovering Laplacian Lattices from $L$-Functions of Graphs
47. Prime and Touchard Congruences of Mixed-Type Bell Numbers
48. A requested analytic proof of an identity of Dixit, Kumar, and Srivastava

arXiv math.NTの新着論文20本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-31/

1. The Sufficient Set of Congruences of Binomial Coefficients for Primality
2. Finite and Symmetric Multiple $T$-Values
3. Diophantine m-tuples of Triangular Numbers
4. Trilinear Kloosterman fractions II: subdyadic intervals and nearly balanced convolutions
5. An Erd\H{o}s-Wintner theorem for second-order linear recurrent bases
6. The Multiplicative Persistence Conjecture: Resolving the \(2\)-Adic Obstruction for Nonzero Even Targets
7. Drinfeld modular forms of higher rank from a lattice-oriented point of view
8. Generalized Fermat equation over number fields
9. Lattice points in high-dimensional $\ell^q$ balls with small radii
10. Rational and integral values of rational functions at rational points
11. Norm Principles for ${\rm Go}(q)$ and ${\rm Spin}(q)$
12. The Algebraicity Problem for Hard-Core Entropy Constants on the Discrete Hypertori
13. Rational torsion on simple genus two Jacobians
14. Harmonic higher weight distributions, Simonis' approach of MacWilliams identity and moments
15. Zero-free columns in character tables of symmetric groups
16. On Frobenius rigidity for motivic cohomology
17. On the number of $2$-dice games with prime power dice-size
18. Arithmetic purity of strong approximation for toric varieties with constant global sections
19. Betti bounds for spaces of curves on varieties and Manin's conjecture for quartic del Pezzo surfaces
20. On Manin's conjecture for quartic del Pezzo fibrations

arXiv math.NTの新着論文30本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-28/

1. Closed geodesics in homology classes modulo sublattices
2. Discrete dynamics of Eratosthenes sieve
3. $k$-Lucas Annulus for Polynomial Zeros
4. A Neighbouring-Denominator Case of the Erd\H{o}s--Mahler Conjecture
5. Period Relations for Theta Products and Elliptic Integral Moments
6. The k-Rank Taylor Family: Canonical Harmonic Lifts, Principal Parts, and Rademacher Series
7. $\mathbb{F}_q$-linear relations among Thakur's multiple zeta values in positive characteristic
8. Torsion-vanishing for Siegel modular varieties via supercuspidal congruences
9. Specialisations of the Burungale-Castella-Skinner main conjecture to $\mathbb Z_p$-lines
10. Two-point correlations of multiplicative functions with dense orbits
11. The Cartesian product of exact approximation sets
12. Ap\'ery-type approximations and irrationality measures for certain $q$-series
13. Resultants of dynatomic polynomials of $x^d$
14. Arithmetic purity of strong approximation for cubic hypersurfaces of large dimension
15. Modular periodicity of the Euler up/down numbers at odd prime powers
16. On variants of P\'olya's conjecture
17. Exceptional covers of the projective line with genus-one Galois closure: arithmetic forms over finite fields
18. The Matrix Pythagorean Equation over $\mathrm{GL}_2(\mathbb{Z})$
19. Birch's theorem over function fields with quadratically many variables
20. On Consecutive Non-primitive Elements over Finite Fields
21. On Piatetski-Shapiro primes from almost primes
22. Integers divisible by a shifted prime in a given interval
23. Delta theory of Anderson Modules II: Hodge-Pink structure
24. Value distribution of multiplicative functions along linear fractional sequences
25. On polynomial expanders with many variables
26. Mixed Tate motives over number fields
27. Isocrystals on unibranch varieties and open immersions
28. The Sharp Spectral Transition for Almost Mathieu Operators via Alternating Resonances
29. A Mixed Robinson--Schensted--Knuth Construction in the Representation Theory of $\mathrm{GL}_n$ over Local non-Archimedean Fields
30. Hankel determinants of Catalan-like sequences

arXiv math.NTの新着論文22本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-27/

1. On the sum of least prime factors in short intervals
2. Transcendence of Tonelli--Shanks Power Modulo Infinitely Large Primes
3. Jacob's ladders, new classes of sum variants of almost linear formula and corresponding $\zeta$-functionals and $\zeta$-equivalents of the Fermat-Wiles theorem
4. The equality cases $P_t(\mathbb{N})=\tfrac12$ for the deconvolved sum-of-digits measures
5. The uniform Littlewood conjecture fails on a set of positive Hausdorff dimension
6. The divisor function for matrices
7. Pseudonullity for fine Selmer groups over multiple $\mathbb{Z}_p^{d}$-extensions
8. Simultaneous Diophantine approximation on the three-dimensional Veronese curve: the complete Hausdorff dimension story
9. Well and badly approximable sets, and rapid winning
10. An elliptic K3 surface X/Q(t) with Mordell-Weil rank 17, I: Formulas for X and base changes of rank 18 and 19
11. Rigid analytic 1-motives and conjugate uniformization of abeloid varieties
12. Arithmetic theta invariants and arithmetic equilibrium measures
13. A Short Proof of a Conjecture Regarding Quadratic Representations of Practical Numbers
14. The Mixed Second Moment of Quadratic Dirichlet $L$-functions with Prime Conductors
15. Intermediate-Range Estimates for Short Weyl Sums and Waring's Problem with Almost Proportional Summands
16. A Boolean polynomial operator for the Collatz $3n+1$ problem
17. The second moment of twisted modular $L$-functions and Dirichlet $L$-functions at the central point
18. Sharp extremal asymptotics for Cusick's sum-of-digits bias at fixed Hamming weight
19. Introduction to the Birch and Swinnerton-Dyer Conjecture
20. An explicit refined Gan--Gross--Prasad identity for Fourier--Jacobi periods of degree 2 Siegel cusp forms
21. Remarks on Vafa-Witten theory, or how to sit on a wall
22. A Categorical Framework for the Direct Integration of Banach Spaces

arXiv math.NTの新着論文24本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-26/

1. Collapsing Fifty Dilogarithm Arguments to Five Terms over $\mathbb{Q}\bigl(u,\sqrt{4-3u^{2}}\bigr)$
2. Poincar\'e duality in Hida families
3. Fourier Spectral Reciprocity and Canonical Hecke $L$-Functions
4. Geometric Realization of Finite Residue Casimirs and Weil Operators via Szeg\H{o} Kernels
5. Sieve dimension and search depth for the Erd\H{o}s-Straus conjecture, $n \equiv 1 \pmod{24}$
6. Modular Forms Related to Real Quadratic Fields as Traces of Cycle Integrals
7. Winning property of counterexamples to Uniform Littlewood's Conjecture
8. A Buium--Coleman bound for the Zilber--Pink conjecture for curves inside abelian varieties
9. Sums of three powerful numbers
10. Infinite continued fractions with a finite alphabet and their applications
11. Polynomial representatives of finite-field maps: a sharp dimensional dichotomy
12. Fourier Coefficients of the Degenerate Eisenstein Series on Symplectic Groups
13. On the Geometry and Shapes of Rank 2 Log Unit Lattices
14. Permutation and exceptionality of rational functions from equivariant elliptic isogenies over finite fields
15. A dual reformulation of the complex sin^2-algorithm: exact identities, descent, and finiteness
16. Contributions to the theory of the Euler eta function
17. Integral quadratic forms over a ring of $p$-adic integers
18. Weil positivity in compact windows: certified two-sided bounds and a Landau--Widom decay law
19. Metaconjugation and Quadratic Forms
20. Oscillation of partial sums of the M\"obius function and zeros of Riemann's zeta function
21. Quantum Algorithms and Hardness for Point-Count Approximation over Finite Fields
22. The Number of Curves of Genus 2 with a Given Refined Humbert Invariant
23. Asymptotic Rounding Laws for Optimal Thresholds in Secretary Problems
24. Kloosterman sheaves and Bessel functions for generic principal series of finite groups

arXiv math.NTの新着論文45本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-25/

1. A non-abelian large sieve and Artin's primitive root conjecture
2. Rational Points and Brownian Motion
3. Dense ascending waves: A resolution of the Alon-Spencer conjecture
4. How many points has an affine algebraic set in residue classes modulo n ?
5. Positive Logarithmic Hausdorff Measures of Exceptional Sets for the $p$-adic and $t$-adic Littlewood Conjectures
6. General Stirling-Ramanujan Constants are exponential periods and applications
7. Prime multipliers of order ten: norm spectra, local charts, and selective lifting
8. Coherent sequences of matrix spectra
9. A Classification of Small MSTD Sets in Arbitrary Fields
10. A note on Zlobin's note
11. Uniformity in rational torsion and small points on abelian varieties
12. The strong form of Van der Waerden's conjecture via twisted Chowla
13. The normalized approximation function for multiple zeta-star values
14. Yun's zeta function and the overorder zeta function for Gorenstein cubic orders
15. Kohnen--Ueda local newforms
16. There and back again with Kaprekar 2-cycles
17. On the constant in Klartag's theorem for lattice packings in high dimensions
18. On uniqueness in equivariant Iwasawa theory
19. Counterexamples to Dujella's conjecture on integral points on the elliptic curve attached to a Diophantine triple
20. The Period-Three Secondary Term in the Mean Value of $L(1/2,\chi_D)$ in the Hyperelliptic Ensemble
21. Cyclotomic norm congruences for zeta values and modular $L$-values
22. Generically Ordinary One-parameter Hyperelliptic Families are Dense
23. Orthogonality Defects of HKZ-Reduced Bases
24. On the binary representation of powers of $3$
25. $p$-adic Equidistribution of Special Loci in a Product of Modular Curves
26. Representations with k-generalized Fibonacci numbers
27. Euclidean Rings
28. A deterministic sin^2-type algorithm for complex cubic irrationalities with exact periodicity certificates
29. Extreme values and logarithm laws for toral translations
30. An elementary note on three consecutive powerful numbers
31. On the graded center of $D(G)^c$
32. Quantitative Logarithmic Chowla Correlations Uniformly over Growing Shifts
33. Power-saving bounds for Thue--Mahler and Mordell equations
34. The classification of generalised Kummer surfaces in positive characteristic
35. Admissibility of Bernstein centers
36. Norm-Query Complexity of Algorithmic Problems in Finite-Dimensional p-adic Normed Spaces
37. The Partition Pairing Theorems I
38. MCSI: A Masked Commutative Supersingular Isogeny Key Exchange with Blinded Ephemeral Keys
39. Marshall Quotients of the Rings $\mathbb Z/n\mathbb Z$
40. A motivic derived Fourier transform
41. On the directions occurring in lattice-line coverings of the integer plane
42. The asymptotic behavior of the rectangle partition function $p(m,n)$
43. An Exact Counting Formula for the Mutual Position of Two Plane Conics
44. The Gao-Zhuang conjecture for the Heisenberg group
45. The number of sum-free subsets of lattice cubes

arXiv math.NTの新着論文13本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-24/

1. A note on least primitive roots
2. Polylogarithmic Chabauty--Kim loci over number fields
3. Maximal and minimal curves of the form $y^3=x^{(q^2+1)/2}+x$
4. Euler characteristic of the Selmer group attached to an Artin representation
5. Complete Resolution Of A Family Of Twisted Thue Equations
6. Arithmetic $\mathcal{D}$-modules over Laurent series fields: the relative case
7. Adjoint Closures of Singular Pairs of Quadratic Forms and a Pfister-Type Criterion
8. Legendre polynomials and complex multiplication, II: class numbers of quadratic fields and genus 2 supersingular polynomials
9. Anabelian Geometry in Families
10. Sums of products of Kloosterman sums to prime power moduli
11. Almost sure upper bound for sums of random multiplicative functions and critical chaos
12. On nearly consecutive sequences without long arithmetic progressions
13. A new lower bound for two-color van der Waerden numbers

arXiv math.NTの新着論文21本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-21/

1. Totally positive field extensions and the pythagorean index
2. An Algebraic Approach to the Fundamental Theorem of Algebra
3. Many Representations as Sums of Three Prime Cubes
4. ${}_5F_4$ evaluations and a family of $\pi^2+\log^2$ identities
5. On the Finiteness of Isolated $j$-invariants for $X_1(N)$
6. Quantitative bounds for sets lacking polynomial progressions with shifted prime difference
7. Arithmetic partial differential operators on ramified extensions of $\ZZ_p$
8. Forced Shadows of an Obstructed Hyperbolic Kac-Moody Denominator
9. Ribet Points, geometric divisibility sequence and order of reductions on semiabelian varieties
10. The irrationality measure of arctan1/2 is at most 8.585166
11. Gap spectra and densities of slow Fibonacci walks
12. Exceptional sets for compositions involving Euler's function,the divisor-sum function and Dedekind's function
13. Simultaneous approximation to pairs of real numbers
14. Modularity theorems for Eisenstein congruences in prime-power level
15. Variation of Iwasawa Invariants for Ordinary Representations
16. Simplex--center configurations in dense subsets of Euclidean spaces and the integer lattice
17. On the number of solutions of systems of diagonal equations through diagonal GP-graphs: the general and the Hermitian-form cases
18. Non-equivalence of pro-$p$-Iwahori invariants
19. Spectrum of the refined Diophantine exponent
20. The arithmetic de Rham stack
21. The Local Langlands Correspondence for Middle Supercuspidal Representations of $p$-adic $\text{GL}(2n)$

arXiv math.NTの新着論文23本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-20/

1. On sums of two primes and six Fibonacci numbers
2. Properties of Kloosterman sums for long Weyl element on GL(n)
3. Rational Solids with Equal Surface Area and Volume
4. Sharp Transitions for Localized Solutions to a Diophantine Inequality
5. Mean Value Estimates for a Real-Exponent Analogue of Waring's Problem
6. Asymptotics of Hecke polynomial coefficients on the Atkin-Lehner eigenspaces
7. On $p$-adic solubility of $Ax^\ell + By^m + Cz^n = 0$
8. Hecke-type action on higher order Herglotz-Zagier function
9. On the Diophantine Equation $p^x+ (2p+1)^y =z^2$ with Consecutive Exponents
10. A Positive Proportion of the Reduced D'Arcais Polynomials is not Hurwitz
11. Universal Ramanujan-type congruences for prime-detecting quasimodular forms
12. The Position-wise Prime Digit Distribution Theorem: A Formal Proof of Position-wise Digit Equidistribution in the Prime Numbers
13. On a classical zero-sum invariant
14. Matchings and product growth in modular abelian independence groups
15. On a conjecture on the Kasami APN function: reductions, structure theorems, a proof for $k\bmod n\in\{1,2,n{-}2,n{-}1\}$, and exhaustive verification for $n\le 13$
16. Finding suitably generic points on curves with an application to the construction of rigid real closed fields
17. Spectral convergence of hyperbolic surfaces and quantum ergodicity
18. Lonely Runners over Function Fields: Quantized Phase--Riesz product
19. Products of trees and ${\rm PGL}_2$-torsors over the punctured affine line
20. Complexity-sensitive additive energy and off-diagonal Young inequalities on bounded-degree algebraic varieties
21. Eureka: Task-Conditioned Meta-Agent Orchestration for Scientific Discovery
22. A simple construction of the automorphic residual spectrum
23. A random walk on p-groups with a symmetric perfect pairing

arXiv math.NTの新着論文18本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-19/

1. Prime-Exponent Transition Geometry and Divisor Barriers Between Consecutive Highly Composite Numbers
2. Algebraic Lattices Arising from Congruence Submodules in Subfields of $p$-th Cyclotomic Fields
3. Mild p-Class Tower Groups of Imaginary Quadratic Fields
4. On Buzzard's Theoren
5. Shifted second moment of Gaussian Hecke $L$-functions $L(s,\lambda^k)$
6. A central limit theorem for prime geodesics on random surfaces of large genus
7. Ribet bimodules and principally polarized superspecial abelian varieties with quaternion action
8. Alternating generalizations of Mizuno's product formula via modified gamma functions
9. Infinitely many primes with a fixed Frobenius field for an elliptic curve over $\mathbb{Q}$
10. On the p-adic Wirsing problem
11. On the integral $2$-adic Tate module of elliptic curves
12. Principal nonsingularity of the Fourier matrices of orders \(70\) and \(143\)
13. Intersecting families and nonvanishing multivariate polynomials over finite fields
14. Squarefree polynomials with missing digits
15. Products of point counts of higher genus curves over finite fields
16. On the Hidden Pascal Symmetry and Moment Constraints of Vector Representatives in Quebbemann's 64-Dimensional Lattice
17. Asymptotics of the Tchoukaillon array and a conjecture of Beluhov
18. A Kernel-Checked Exclusion Certificate for Erd\H{o}s Problem 647

arXiv math.NTの新着論文35本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-18/

1. A descent-set obstruction for the Casas-Alvero conjecture
2. Exponential sums over primes
3. Reciprocity for The Short Twisted Second Moment of The Riemann Zeta Function
4. Bounding The Number of Zeros Near the Central Point in Families of Cuspidal Newforms
5. Transcendence of continued fractions over function fields and a quantitative version of Uchiyama's theorem
6. Algebraic geometric framework of Rogers--Ramanujan identities
7. Interlacing for zeros of the Serre derivative of Eisenstein series
8. Positive quasimodular forms and the sign uncertainty principle
9. Singular-weight Conway-invariant Jacobi forms of index four
10. Proof of a Conjecture on Primitive Quartic Polynomials over Finite Fields
11. Formal finite multiple zeta values
12. Cycles of supersingular elliptic curves for pairing-based proof systems
13. Beyond endoscopy for $\mathsf{GL}_2$ over $\mathbb{Q}$ with ramification 5: cancellation theory
14. The principal series 2-representation for $\mathrm{GL}_n\times\mathrm{GL}_n$ over a 2-dimensional local field
15. An exact formula for Erd\H{o}s' problem 1005
16. Hausdorff dimension of $\tau$-approximable points on self-similar sets in $\mathbb R^d$
17. Large values of quadratic character sums
18. Better than square-root cancellation in Piatetski-Shapiro sequences
19. Weighted singular vectors in common-base self-similar sets
20. On the Hausdorff dimension of the difference sets between typical and normal numbers
21. Height Rigidity for Entire Functions
22. On integers that are representable as the sum of two units
23. On the residual Eisenstein cohomology of unitary groups
24. Simple and distinct zeros in a prime-modulus Dirichlet family at mesoscopic shrinking height
25. Superspecial Points on Shimura Curves
26. A dynamical generalization of Chowla's conjecture on average
27. The multiplication table problem in large dimensions
28. Oort's conjecture on supersingular abelian varieties in odd characteristic
29. Subconvexity of Short $k$-Free Exponential Sums
30. Galois descents of certain multiple polylogarithms
31. M\"obius Covariance and Coefficient Duality: From Bernoulli Series to Enumerative Applications
32. The equality between the Erd\H{o}s-Ginzburg-Ziv constant and the short product-one constant for finite nonabelian groups
33. A six-functor formalism for syntomic cohomology
34. Degrees of Genus-Two Split-Jacobian Loci and Humbert-Form Reconstruction
35. Matrix group $\Lambda$-distributions

arXiv math.NTの新着論文19本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-17/

1. On the Existence of Hyperelliptic Curves over $\mathbb{Q}(T)$ with Certain Jacobian Ranks
2. More than two thirds of the zeta zeros are simple and on the critical line
3. Some Dwork-type $q$-supercongruences from a $_6\phi_5$ summation formula
4. $p$-numerical semigroup of the sequence of consecutive odd integers
5. A structural trace identity and certified spectra for the Richelot-Brandt graph
6. A Kubilius model for sieve-theoretic sequences
7. Ratio of sum of digits functions in two bases
8. Hurwitz class number relations and mock modular forms
9. New Congruences Involving $p$-adic dual sequences
10. Shimura curves of discriminant 14 and 15 and associated Heun Functions
11. The inverse Galois problem of iterated Galois groups and their fixed-point proportion
12. Intensional semantics for comparison problems in arithmetic geometry
13. Multiplicative chaos from random multiplicative functions
14. Algebraic curves admitting automorphism groups of large prime square order
15. Sharp refined-direction Kakeya estimates in finite Heisenberg groups
16. Counting non-attracting subtrees and the equidistribution of repelling points
17. Semi-abelian reduction of Albanese varieties
18. Near diagonal additive energy bound for points on algebraic surfaces
19. Compressive Domains and a Bound for the Number of Components of the Fixed Locus of a Self-Map of the Berkovich Line

arXiv math.NTの新着論文31本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-14/

1. On Waring--Goldbach problem with mixed powers
2. Generalized Addition Theorems for the Jacobi Elliptic Functions
3. A conditional arithmetic obstruction to the prime numbers as a spectrum of a probability measure
4. Finding all cospectral mates over a number field
5. Special Values of Shifted Dirichlet Series from an Adjoint Map on Almost Holomorphic Modular Forms
6. Density bounds for permutations avoiding monotone arithmetic progressions
7. Escalations and criteria over real quadratic fields
8. Algebraic constructions of point sequences with quasi-uniform two-dimensional projections
9. Uniform bounds on prime levels of abelian division fields of elliptic curves over number fields without rationally defined CM
10. Finite-Sum Realization of Archimedean Asai and Exterior-Square $L$-Factors
11. On the Lorenz-Fibonacci sequences and substitutions
12. Cyclic permutations of large subsets with polynomial values in multiplicative subgroups of finite fields
13. A study of degenerate Bernoulli and Euler numbers via operators
14. Analytic rank one propagation in Hida families
15. On $\mathcal{B}^4$-almost periodicity for a class of arithmetical functions
16. Generalizations of the Christoffel-Darboux formula and congruences involving Ap\'ery-like numbers
17. Infinitely many elliptic curves over $\mathbb{Q}(i)$ of exact ranks 4 and 6 with $j$-invariant 1728
18. Asymptotic Analysis and Phase Transition of the Bessel-Kuznetsov Transform with an Oscillatory Phase
19. On a conjecture of Corradi and Katai
20. Convolution-type Bombieri-Vinogradov theorem with well-factorable Weights, and its applications
21. Local Minkowski units in non-abelian extensions with cyclic Sylow $p$-subgroups
22. Some convolution identities for mock modular forms arising from the theory of holomorphic projection
23. Gross vectors modulo 2 and elliptic curves of prime conductor
24. Intersective Polynomials and Universal Separation of Divosor Profiles
25. The distribution of $k$-free ideals in ray class groups
26. Multiplicative Subgroups of Prime Fields Are Not Sumsets
27. The Five Distance Theorem For A Convex Norm
28. Tame fundamental groups of rigid spaces
29. Euclidean SVP is deterministically NP-hard to approximate within any constant factor
30. Spectral and Isoperimetric Bounds on Flat Tori
31. Optimal local convergence criteria for integer and Gaussian integer continued fractions

arXiv math.NTの新着論文18本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-13/

1. The motivic Selmer scheme of the thrice-punctured line
2. Upper bound for the moment of shifted values of cubic $L$-functions over function fields
3. Galois Symbols for a Jacobian and Multiplicative Groups
4. Equalities among simplest quartic fields: a complete classification
5. Height lower bounds for elements of highly composite rings
6. A $p$-part Birch and Swinnerton-Dyer Formula over Totally Imaginary Quadratic Extension of Totally Real Fields
7. Hasse-Witt invariants for trace forms of Jacobi polynomials
8. Duality formulas for $\widehat{\mathcal{Q}}$-multiple zeta values
9. The 196560 auxiliary-function conjecture for the Leech lattice
10. Multiplicator freeness for restricted-ramification Galois groups over global function fields
11. Power sums and Siegel-type zero-free regions for L-functions
12. A Multiplicative Fourier Proof of the Length-Four Index Conjecture
13. On The Spectral Properties of Discrete Landscape Functions
14. Visible Measures along $\Omega(n)$ and Distribution of Horocycle Orbits
15. A Proof of a Conjecture on Fixed Perimeter Partitions
16. Edit distance exponents for irrational rotations
17. Invariant Functions on $p$-divisible Groups and the $p$-adic Corona Problem II
18. Near optimal three-fold additive energy bound for points on convex curves

arXiv math.NTの新着論文16本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-12/

1. On the Squarefree Values of Degree-$2q$ Polynomials
2. An omega result for the first sign change of coefficients of symmetric power $L$-functions of Hecke-Maass cusp forms
3. A proof of a weighted sum conjecture for finite multiple zeta values of level two
4. Average root numbers in two isotrivial families of elliptic curves
5. Permutation polynomials from the trace functions
6. Bockstein Spectral Sequences and Applications to the Tame Fontaine Mazur Conjecture
7. Distinguishing elliptic curves modulo $p$ and identifying images of product representations
8. A canonical construction of signed $p$-adic $L$-functions for non-ordinary modular forms of weight $\leq p+1$
9. Equationless quadratic Chabauty for non-split Cartan modular curves
10. A double-sum analogue of Whipple's summation formula and a restricted sum formula for multiple binomial sums
11. Kneserized Anticoncentration and Reverse Absorption for Graham's Rearrangement Conjecture
12. Classification of Fourier summation formulas on a horizontal strip
13. Introduction to Universal Equations and Characteristic-free Resolution
14. Mutation-preserving generalized cluster algebras and Laurent mutation invariants
15. Finite monodromy groups in degenerating families and the stability degree of curves
16. Poincar\'e \`a la Makdisi

arXiv math.NTの新着論文37本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-11/

1. Zeta zeros of function fields heuristically equidistribute as genus goes to infinity
2. Sharp vertex connectivity of the Markoff graphs modulo $p$
3. Positive Lower Density for Hofstadter's $ab-1$ Problem
4. On the Emerton-Gee stack of potentially semistable representations
5. Representations as Sums of Icosahedral and Dodecahedral Numbers: Proof of Pollock's Conjectures
6. Which numbers are $u$-invariants of perfectoid fields?
7. Binomial coefficients coprime to 6
8. Short Second Moment of $\mathrm{GL}(2)$ L-Functions via Trivial Delta
9. Equidistribution for semiabelian varieties over number fields
10. Machine-Guided Recurrence Boundary Theory for Nahm Sums
11. On Sun's Conjectures for Truncated Jacobi-Symbol Determinants via Supersingular Elliptic Curves
12. Proofs of the Conjectures on $SOME(n)$ and $DSOME(n)$ Functions Related to Integer Partitions
13. The Mathieu group $M_{23}$ is a Galois group over $\mathbb{Q}$
14. A new hyperbolicity wedge and a joint semicircle limit for Jensen polynomials of Riemann's $\xi$-function
15. Twisted Bernoulli Zeros in Quasi-Linear Time: Distribution, Depth, and Explicit Hilbert Class Components
16. On some representations of Metacyclic groups whose integral forms can be computed from a single residual representation
17. Modular resurgent structures for vectors
18. Sharp Bounds for Rational Points Near Space Curves
19. The minimal obstruction modulus for quadratic forms
20. Plancherel and Poisson summation formulae for a family of affine $\Psi$-bundles
21. A Sharper Explicit Result for the Sum of Two Almost Primes
22. A proof of a conjecture on permutation polynomials
23. An analogue of Hirose's relation for finite multiple harmonic $q$-series at roots of unity
24. Counting metacyclic fields
25. On the $\beta=2$ Partition function for Dirichlet $L$-functions in the $q$-aspect
26. Large class of many-to-one mappings over quadratic extension of finite fields
27. Uniform stratified vanishing and equidistribution on $\mathbb{G}_m^d$
28. On the Godement-Jacquet functional equation for finite matrix monoids
29. The Borel complexity of non-Archimedean operator ranges
30. Some new results for Andrews' Kimberling partitions
31. Hankel Transform and $(\alpha,\beta)$ Somos-4 Sequences
32. Jacobi Endpoint Pencils and Sharp Interlacing for Centered Binomial Samples
33. A note on the partition function of a rectangle
34. Restricted generalized Schur numbers
35. Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages
36. A proof of the cyclotomic conjecture and the non-existence of almost Moore digraphs
37. Varieties with prescribed fundamental group schemes

arXiv math.NTの新着論文15本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-10/

1. Refuting a Conjecture of Umans and Wang on Arithmetic-Progression Divisor Covers
2. Squarefree numbers in short intervals: explicit and formalized
3. Anticyclotomic Iwasawa theory of CM elliptic curves at ramified primes
4. A Combinatorial Approach to Vorono{\"i} Theory
5. An extension of Ramanujan-Guinand identity for the Dedekind zeta function and a new formula for $\zeta_\mathbb{F}(2)$ and $\zeta_\mathbb{F}(2m+1)$
6. On semi-stable integral models for Shimura varieties
7. Modularity of Higher Theta Series III: Proof of the Modularity Conjecture
8. Towards the Fontaine--Mazur conjecture for GL(2)
9. Heath-Brown identities for fractional powers of $\zeta$
10. On the Existence of Primitive Polynomials $f(x)=g(x)+ \lambda$ over Finite Fields
11. Siegel zeros and small gaps between zeros of the Riemann zeta function
12. $\Delta$-separated Sidon sets in additive number theory
13. Universality for Random $p$-adic Polynomials and Random Matrices Via the Resultant Distribution Method
14. A three-dimensional corner configuration involving the Omega function
15. Arithmetic Properties of Mixed Stirling Numbers of the second kind

arXiv math.NTの新着論文19本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-07/

1. Rigidity of Averages over the Two Largest Prime Factors
2. Explicit Algebraic Numbers all whose Integer Parts of Powers are Composite
3. The sesquicentennial of the prime number $2^{127} - 1$
4. Trianguline representations and locally analytic principal series of ${\rm GL}_2({\mathbb Q}_p)$
5. Asymptotic uncorrelations between functions with squarefull kernel and functions of invariant average
6. Modularity of Point Counts for the Curves $X^a=Y^b$: New Rogers--Ramanujan Identities
7. Iwasawa invariants and exceptional pairs of certain abelian fields
8. Generalised Gauss--Kuzmin Distribution for Klein sails in $\mathbb R^3$
9. Hearing Tamagawa Factors modulo $q - 1$
10. Hybrid Weyl Subconvexity over Imaginary Quadratic Fields
11. Bounds for moments of twisted quadratic characters of prime modulus
12. Periods of E-operators
13. Strong Weil Degree Divisibility at Higher Levels
14. Average analytic rank for the $L$-functions of the elliptic curves $y^2=x^3-dx$
15. The good reduction of generalized Kummer surfaces in the non-supersingular case
16. On the motivic cohomology of some singular rings
17. New central $q$-binomial identities
18. Higher-Order Cyclotomic Congruences for $q$-Secant and Generalized $q$-Euler Numbers
19. Exact renewal laws for minimal common-denominator profiles in simultaneous Laurent-series approximation

arXiv math.NTの新着論文16本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-06/

1. Rational spanning sets of level-one cusp forms from Eisenstein series at prime levels
2. The distribution and the structure of the maximum of partial sums in families of trace functions
3. The $5$-divisible integer group determinants for the elementary abelian group of order 25
4. On the Burgess bound and Pythagorean triples involving primitive roots
5. Powers as Fibonacci Sums
6. Regularized Multitangent Functions and Reduction Theorem
7. Construction Of Non-Odd Galois Representations With Large Image
8. On the $L^2$ restriction norm of large level
9. A proof of the Freiman-Lev conjecture
10. Adelic framed form class groups and explicit class field theory
11. Quantitative Khintchine on the parabola with non-monotonic approximation functions
12. Chebotarev geodesic theorem: non-split case
13. An Integral Mean Value Theorem for Weyl Sums over Broken Arcs
14. Weyl Subconvexity for $\mathrm{GL}_2$ with Simple Supercuspidal Ramification
15. Dualizable Additive Categories
16. Sparse Random Covers and Growth of Torsion in First Homology

arXiv math.NTの新着論文16本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-05/

1. A Classification of Multiply Monogenic Quartic Orders
2. Counting in Vieta graphs over $\mathbb{F}_p$
3. On pairs of primes with small order reciprocity
4. Admissible Pairs: A Variation to Pollock Conjectures
5. Mellin Transform Formulas for Anderson Modules and Hints of Modularity
6. Erd\H{o}s-Moser Equation in Arithmetic Progressions
7. Explicit Jordan decompositions for ideal lattices in CM fields
8. No three algebraic conjugates of degree sixteen sum to zero
9. An upper bound for counting algebraic tori over $\mathbb{Q}$ by Artin conductor
10. On the distribution of $\phi(\psi(n))$ and $\psi(\psi(n))$
11. Non-split Cartan curves and a characterization of fake elliptic curves
12. On Diophantine equations over the integer rings of quadratic fields
13. The extended Fargues--Scholze spectral action
14. Murphy's law in non-abelian Hodge theory
15. Strichartz estimates for quasi-periodic functions on long time intervals: An arithmetic approach
16. Refined upper bounds on Schur-like numbers

arXiv math.NTの新着論文54本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-04/

1. Random Multiplicative Functions with Periodic Weights
2. Ljunggren--Jacobsthal and Bailey-Type Congruences for Rectangular Gaussian Binomial Coefficients
3. Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields
4. Positive rational series for reciprocal powers of Catalan's constant and Dirichlet beta values
5. Negative bias in moments of the Legendre family of elliptic curves
6. Machine learning the arithmetic of Boyd's Mahler measure conjectures
7. Faster Deterministic Integer Root Finding for Integer Polynomials
8. Dynamical Canonical Heights and Finite Trees
9. The Minimal Degree of Salem Numbers with Negative Trace
10. Cycles for Rankin-Selberg $L$-functions, I: automorphic periods
11. de Rham theory and locally analytic vectors
12. Arithmetic of elliptic curves induced by regular Diophantine triples
13. Lattice point sumsets and asymptotic approximate groups
14. Weights in \'etale cohomology over mixed-characteristic local fields and applications to anabelian geometry
15. Bilinear Kloosterman sums over small boxes and uniformity of a random walk
16. Distribution of simplices in the discrete and continuous settings
17. On binomial order and primitivity of irreducible quadratic polynomials over finite fields
18. Murmurations of quadratic and cubic characters over function fields
19. Weighted averages of Bernoulli polynomials and the Gamma function over regular integers modulo $n$
20. Families preserving isomorphisms via techniques in anabelian geometry: with an application to a generalized Neukirch-Uchida theorem
21. Nine-distance theorem and growth of best-approximation denominators
22. A Coates-Sinnott-type Theorem for First Derivatives of Artin $L$-Functions
23. Bounds for Mertens Sums
24. Algorithmic universal \'etale $(\varphi,\Gamma)$-modules
25. On the Petersson norm $\langle\theta_{\psi},\theta_{\psi}\rangle$
26. Constructing Self-Regulating Field Theoriesfrom Primal Wave Fields without Background Manifolds:The Emergence of the Coordinate Continuum
27. A New Characteristic-Uniform Model for Elliptic Curves -- Theory, Arithmetic, and Applications
28. Factorial residues modulo a prime: beyond the square-root bound
29. Integral Representations and Asymptotics for a Family of Areal Mahler Measures
30. The Local Four-Square Problem over \(\mathbb{Z}_{p^k}\)
31. Every quasiperfect number has at least eight distinct prime factors
32. Multiple Zeta Values
33. On the $L^6$-norm of holomorphic Hecke eigenforms
34. Mahler measures at interior CM points: proofs of two conjectures of Samart
35. Samart's conjecture n_4(81)=40M_7: the exact CM evaluation and the two obstructions. A status report
36. An intermediate conjecture between Goldbach and Dubner: every even number is the sum of a prime and a twin prime
37. Isogeny graphs of elliptic curves in characteristic zero
38. Automorphic functions for square-zero extensions of curves over finite fields
39. Additive decompositions of multiplicative subgroups in prime fields: a self-contained approach
40. Associated graded modules for modular representations of quaternion algebras
41. Identities involving the number of missing integers in partitions - combinatorial proofs
42. Localization and elliptic motivic relations
43. Fixed Perimeter Analogues of Several Partition Results Related to Parity
44. Arithmetic hypergeometric $\mathcal {D}$-modules and exponential sums on reductive groups
45. The finitude of the fibers of the complementary Bell numbers
46. Collinear Interior Lattice Points in Triangles Satisfying $B(T)\in\{4,5\}$
47. Convolutive sequences, II: Parametrizations
48. Schur--Plucker Geometry of the MDS Locus for Principal-Ideal Codes
49. Square-Difference-Free Sets beyond the Three-Quarter Barrier
50. Intertwining Operators for Siegel Parabolics over Finite Fields
51. The catenary degree of monoids of product-one sequences
52. Square-integrability of holomorphic differential forms on locally symmetric varieties
53. Counterexamples to the Minimum Period Conjecture for Restricted Partition Functions
54. Comparing local-global obstructions on algebraic stacks

arXiv math.NTの新着論文10本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-03/

1. Multiplicative dependence in the sumset of multiplicative groups
2. The Fine-Structure Hierarchy of Prime Biases and the Universal Dominance of $-1 \pmod N$
3. Small points in radical extensions of number fields
4. Generalized Wieferich primes and monogenic trinomials
5. An Introduction to p-adic Hodge Theory
6. A sharp almost sure upper bound for partial sums of random multiplicative functions
7. On the size of $h$-fold sumsets
8. The least quadratic residue and integers represented by quadratic forms
9. On Generalized Chebyshev polynomials
10. Slice and Partition Rank Criteria for Polynomial Zero-Avoidance

arXiv math.NTの新着論文23本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-31/

1. The exceptional set of the Goldbach problem
2. Multivariate counting of wild abelian extensions
3. On some Diophantine and Ergodic properties of the Schneider map over function fields
4. On the greatest common divisor of $n, \lfloor \alpha_1n\rfloor, \lfloor \alpha_2n^2\rfloor, ..., \lfloor \alpha_kn^k\rfloor$
5. An Asymptotic Bound for Non-covering Congruence Systems over Fq[x]
6. Perfect $2$-codes over arbitrary alphabets
7. Schur Eisenstein series and Schur MacMahon series
8. Irrationality of finite logarithms in a congruence-class ad\`ele ring
9. On a question of Gowers related to Littlewood's conjecture
10. On the Gow--McGuire Conjecture for Primitive Quadratic Polynomials
11. Random linear configurations in dense sets and primes
12. Regularity of Diophantine quadruples over $\mathbb{Q}(i)[X]$
13. Euler-type Recurrence Relations for Partition Functions with Congruence Conditions
14. Eventually greedy best Egyptian underapproximations of rational numbers via optimal control
15. Ginzburg's conjecture on the unramified computation of Eulerian integrals
16. Vertex volumes, lattice-minima tails, and height zeta functions for the standard arithmetic quotient of $\operatorname{PGL}_d$
17. Deformation of the absolute Galois groups of number fields
18. Schwartz spaces on L-monoids: non-Archimedean
19. Sumsets and generalized arithmetic progressions in multiplicative subgroups
20. $\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns
21. Proof of a Conjectured Ramanujan Type Master Theorem for Powers of the Cosecant
22. Types and collapse for cuspidal representations of groups acting on trees
23. Franklin's identity for $n$-color partitions and companion Beck-type identities

arXiv math.NTの新着論文18本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-30/

1. On purity of Anderson t-modules
2. Inclusions between p-bounded crystalline loci in dimension two
3. Bhargava Gamma functions for determinant-admissible sets
4. On the transcendence of twisted special $L$-values at non-negative integers in characteristic $p$
5. Improved Bounds for Distinct Multiples in Intervals
6. On Oliver's relations between infinite series and infinite products
7. On a Question of Lehmer concerning the Comtet Numbers
8. On the higher algebraic $K$-groups of arithmetically equivalent number fields
9. Explicit mock Heegner points and BSD formula on certain Mordell curves
10. Dimensions of Orbit Closures and Discrepancy for Dynamical $p$-adic Sequences
11. Kuroda's Class Number Formula
12. On a problem of minimal additive complements for not eventually periodic $S$-difference sets
13. On the second moment and non-vanishing of central values of Hecke $L$-functions of $r$-th order characters
14. Formally certifying number field invariants
15. Fuglede's Conjecture on Cyclic Groups of Square-Free Order: The Case of Rapidly Growing Prime Factors
16. Asymptotics of the spectral determinant of the weighted Laplacian for a sequence of compact Riemann surfaces of infinitely growing volume
17. Splitting Brauer classes by genus one curves over number fields
18. A topological interpretation of numbers

arXiv math.NTの新着論文23本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-29/

1. Extremal Chowla sets and their linear analogues: A human-AI mathematical investigation using Co-Scientist
2. Transcendence of multivariate Mahler functions and algebraic relations between their values
3. Twisted automorphic descent to odd GSpin groups and applications
4. On certain $D(9)$ and $D(64)$ Diophantine triples
5. The Explicit Hypergeometric Modularity Method III
6. Diagonal cycles on Shtukas and the adjoint $L$-function
7. On the Vanishing of the Brauer-Manin Obstruction for Normic Bundles
8. Beyond endoscopy for the symmetric square representation: The simple trace formula case
9. Extreme values of quadratic Dirichlet $L$-functions with prime-related moduli
10. On an asymmetric additive energy inequality
11. Hypernatural numbers in arithmetic Ramsey theory
12. Refined Humbert Invariants in Supersingular Isogeny Degree Analysis
13. An Asymptotic Formula in Waring's Problem for Seventeen Fourth Powers with Almost Equal Summands
14. Multiplicative subgroups are not restricted sumsets
15. Intersection Cohomology of Igusa Stacks
16. $d$-Translated Unit Sensitive Primes
17. Collision of Orbits for Families of Polynomials Defined over Number Fields
18. Local Moments of M\"obius Fourier Polynomials and the Riemann Hypothesis
19. A Criterion for Equidistribution along the $\Omega$ Function over Polynomial Sequences with Applications
20. Graph integrals, Feynman periods, and single-valued multiple zeta values
21. Kernel-Checked Exclusions for the Erd\H{o}s-Selfridge Odd Covering Problem: Any Odd Covering of $\mathbb{Z}$ Has lcm Exceeding 10000
22. Solution of Erd\H{o}s problem $\# 443$
23. Iterate Wronskians over $\mathbb{R}^d$ as $N$-ary brackets on $\mathbb{R}[x^1,\ldots,x^d]$: the $N$-bonacci numbers bound the highest total degrees

arXiv math.NTの新着論文31本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-28/

1. Jittered sampling and probability measures
2. Tadpole Nahm sum as a Wronskian
3. Unshared zeros of Dirichlet $L$-functions
4. On the Frobenius Number of Quotients of Numerical Semigroups
5. Finite length for unramified $\mathrm{GL}_2$: beyond multiplicity one, non-semisimple case
6. On the role of higher roots in prime ideal races
7. Explicit Twisted Hilbert Class Components Beyond Classical Irregularity
8. On the Comparison of the D-new Modular Degree and the Shimura Degree of Modular Abelian Varieties
9. Modularity of Nahm Sums Dual to Zagier's Rank-Three Examples
10. A lower bound for the distance between CM points on Shimura curves
11. Matrix Kloosterman sums and product-trace estimates for semisimple algebras
12. On the automorphisms of numerical power monoids
13. Optimality of Wouter van Doorn's Upper Bound for the Mayer-Erd\H{o}s Farey Problem
14. Self-Referential Leading Digits of Exponential Sequences: Arithmetic Structure and Certified Search
15. Algebraic values of transcendental power series with geometric coefficient moduli
16. Larger sieve with height function and uniform bounds for integral points on curves over number fields
17. Slowly Divergent Trajectories for Weighted Singular Vectors in R^2
18. Decision trees, Frobenius traces, and Weierstrass coefficients of elliptic curves
19. Signs of Square-Free Fourier Coefficients of Half-Integral weight cusp forms and the Congruent Number Problem
20. Bilinear forms with Kloosterman sums via quadratic characters
21. On $C^k$-functions mapping $\mathbb{Q}$ into itself and Mahler's problem on Liouville numbers
22. A Salem-Spencer-Type Construction for Large Subsets of Integer Grids with No Isosceles Right Triangles
23. Non-isomorphism of rings of integer-coefficient holomorphic functions on disks of varying radius
24. Tiling a triangle into a prime number of congruent triangles
25. Additive Bases from Primitive Dyck Words: Regular Underapproximations, Motzkin Coding, and Digit Lifting
26. On the Thickness of Infinite Generalized Sidon Sets, II
27. Beyond the Adams Conjecture
28. Cyclic codes and cyclically covering subspaces
29. Multiplicative irreducibility of shifted multiplicative subgroups in the extremal case
30. Simply branched covers of curves and wild conductor exponents
31. On the problem of large gcd for disjoint residue classes

arXiv math.NTの新着論文11本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-27/

1. Explicit bounds for Buchstab's function
2. A More Efficient Algorithm for Finding the Number of Permutations of $\mathbb{ZZ}/n\mathbb{ZZ}$ with Distinct Partial Sums
3. Factorial Calculi and the Canonical Stirling Defect of the Prime Bhargava Factorial
4. Densities of arithmetic Hecke triangle group orbits
5. Explicit height bounds on modular polynomials for the elliptic $j$-invariant, cube root of $j$, and Weber modular function $\mathfrak f$
6. Prime-Interval Algebras
7. Congruences for the coefficients of MacMahon-like $q$-series
8. Playing with additivity conditions in multiplicative functions
9. Autonomous disproofs of the sum-product conjecture over $\mathbb R$ with GPT-5.5 Pro
10. Exterior power sums
11. Some aspects of the spectral theory with twisting representations

arXiv math.NTの新着論文18本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-24/

1. A problem on sumset sizes of sets of lattice points
2. Infinite Sidon-type sets for zero-sum linear forms
3. Inverses of Fibonacci and Lucas Numbers via Rational Indices
4. Zeros of the Dirichlet series of even zeta values
5. On a Diophantine Equation with Jacobsthal and Fibonacci Numbers
6. Murmurations of quadratic Hecke $L$-functions of the Gaussian field
7. On $v_2(q),v_3(q),v_4(q)$, and Andrews' Conjectures 5 and 6
8. On structured cosine sums and applications
9. Fibonacci, Dirichlet, and Gauss in a single sum
10. The $p$-rationality of $\mathbb{Q}\left(\sqrt{-(kp+m)}\right)$ and $\mathbb{Q}\left(\sqrt{p(p+1)}\right)$
11. On the Fractional Parts of Polynomials Modulo $p$
12. Zeta functions of $\mathrm{PGL}_n$ over non-Archimedean local fields
13. A Weighted Sum Formula for Double Eisenstein Series
14. Statistical properties of Hecke correspondences
15. Simultaneous non-vanishing of Dirichlet $L$--functions, II: Weighted central limit theorem
16. Absolute minimum of a height associated to a semipositive adelic line bundle
17. Generic ordinarity for abelian coverings of the projective line
18. Arithmetic progressions in a random set on a budget

arXiv math.NTの新着論文12本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-23/

1. Integral magneticity of the level-two K3 packet: CM theta lifts and a 2-isogeny trace contraction
2. Additive and multiplicative densities, prime valuations and symbolic models
3. Multiplicative dependence modulo subsets
4. The Pila-Zannier strategy for Drinfeld modules and Drinfeld modular curves
5. On the value distribution of the Riemann zeta-function with general shifts
6. Extreme values of quadratic Dirichlet $L$-functions
7. Non-Archimedean Rigidity and Uniformity for Common Preperiodic Points
8. Rational Spectra for Finite Hadamard Pairs and Bounded Spectral Sets on the real line
9. The Significance of Proposition II in Galois' M\'emoire, The Origin of Galois Automorphisms
10. The inverse problem for the Steiner-Wiener index of trees
11. Automorphism groups of curves with simple Jacobians
12. The sharp exponent for the minimal distance problem

arXiv math.NTの新着論文16本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-22/

1. On a certain arithmetic function defined via Bernoulli numbers
2. Binary quadratic forms and elliptic curves with analytic rank one
3. Divisor moments of polynomials in Fourier coefficients of modular forms
4. On Diophantine $m$-tuples related to primitive elements of finite fields
5. On the digits of the sum of proper divisors
6. A Distinct Covering System with Minimum Modulus 7 and Minimal Least Common Multiple 10080
7. On canonical roots of fractional ideals
8. On the $\mathcal{A}$-transcendence of a Champernowne-type constant
9. Unlocking the Wronskian Tower: A Simplification of the Holomorphic Modular Bootstrap
10. Cyclic and Constacyclic Codes Over Z4+iZ4
11. A Local Classification of Four-Element Multiple Sumsets
12. Zero-cycles on surfaces dominated by products of hyperelliptic curves
13. Generic polar divisors and flag residues for root-system zeta functions
14. Bayesian Sequential Quantum Amplitude Estimation for Rare-Event Structural Failure Probability
15. Minkowski dimension and content of complex continued fractions
16. Exploiting Load/Store Leakage of Sparse Vectors for Key Recovery in HQC

arXiv math.NTの新着論文29本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-21/

1. Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions
2. A Complete classification of the rank of a certain family of elliptic curves
3. Non-ordinary primes and congruences for weakly holomorphic modular forms of level 2
4. Density of Unicritical Polynomials over Local Fields with Rational Periodic Points
5. Arithmetic properties of the 2-color overpartition function $\overline{p}_\ell(n)$
6. Solutions to Two Problems of S\'ark\"ozy and S\'os on Additive Representation Functions
7. Counterexamples of Friedlander--Iwaniec dual sums conjecture
8. An explicit uniform cubic wedge for consecutive Toeplitz minors of the Riemann xi coefficients
9. Twisted Siegel-Weil formulas for $\mathrm{GL}_2$ over non-Galois quartic CM fields
10. A Modular Form Proof of the Irrationality of $\zeta\left(3\right)$
11. On the average number of subgroups of the group ${\Bbb Z}_{n_1}\times {\Bbb Z}_{n_2}$
12. A survey on moments of a class of error terms
13. Consecutive non-square non-primitive tuples in finite fields
14. Torsion of rational elliptic curves over $\Z_p$-extensions of quadratic fields for $p\geq5$, with a slope analysis for $p=3$
15. On Erdos-Falconer distance problem in even dimensions
16. Galois-invariant N\'eron--Severi ranks of Fermat surfaces over number fields: a Galois module, closed forms, a threshold, and exact tables
17. Quadratic residue patterns of length 4 and 5
18. Diophantine analysis and the Braid group ${\bf B}_3$
19. On some sums involving small arithmetic functions
20. Betti-Whittaker periods under duality: variations and applications
21. Jacob's ladders and new $\zeta$-functionals and corresponding $\zeta$-equivalents of the Fermat-Wiles theory based on sums of elementary $\zeta$-pulses
22. Bounded trajectories of quasi-rays on homogeneous spaces and Diophantine approximation with weight functions
23. A short survey the game Bulgarian solitaire and related games
24. A positive answer to the Owings's sumsets question
25. Space of norms on locally algebraic representations
26. Counting subsets of integers free of arithmetic configurations
27. Quantitative Oppenheim in signature $(2,2)$ via determinant values
28. Determinant values on lattices
29. Fricke's trace identity and spin groups

arXiv math.NTの新着論文16本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-20/

1. A counterexample to a conjecture of Thakur on Carlitz-Wieferich primes
2. The Second Term for Strongly 2-Primitive Sets
3. A weighted entropy approach for the quadratic inverse large sieve conjecture
4. Finiteness of the Tate-Shafarevich group over function fields for groups of multiplicative type
5. Sets of unit fractions without two members whose average is a unit fraction
6. Indecomposable translates and degree-$d$ points
7. On the existence of Newman and Littlewood multiples for certain integer polynomials
8. Improved bounds for multiplicative functions in almost all short intervals
9. Arithmetic unlikely intersections in powers of the multiplicative group
10. A comment on the number of $k$-th powers inside arithmetic progressions
11. Upper bounds for moments of analytic ranks of elliptic curves over number fields
12. An improvement on the largest prime factors of consecutive integers
13. Equidistribution for abelian extensions of global fields
14. Defining reduction types of curves via minimal regular and minimal normal crossings models
15. Conjectural Decidability of the Skolem Problem
16. Singular points for cone actions on the product of certain homogeneous spaces

arXiv math.NTの新着論文15本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-17/

1. Beyond the Riemann Hypothesis bounds: A pair-correlation approach to the least prime in arithmetic progression and the smallest quadratic non-residue
2. The Spine: A Supersingular Highway
3. The First Moment of Dirichlet L-functions over Generators of the Character Group
4. Minimal degree of an isogeny between a supersingular elliptic curve and its conjugate
5. Multiple Clausen values and deformed Ap\'ery-like series
6. Equidistribution and the torsor method
7. On the Log-Concavity of the D'Arcais Polynomials for Normalised Functions
8. Double $L$-values of Negative Weight Admitting Series Representations
9. On a character-twisted analogue of Sch\"{a}ffer's equation
10. A Bombieri-Vinogradov theorem for exponential sums over products of k primes
11. Formality for rigid-analytic spaces satisfying the weight-monodromy conjecture
12. Aperiodic tile sets from Sturmian lattices
13. Several families of incommensurable noncompact hyperbolic Coxeter polytopes
14. Aperiodicity and subword complexity in the binary expansion of powers of three
15. Asymptotic Brill-Noether Existence at the Half-Canonical Degree: Energy Pairing, Cheeger Inequality and Covering Radii

arXiv math.NTの新着論文17本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-16/

1. A minimal modularity lifting theorem for Siegel modular forms
2. Beyond Mock Modularity: Elliptic Corrections for Higher Dyson Ranks
3. On the Second Moment of $ L (1/2, \mathrm{As}(f) \times \phi)$
4. Study on Morgan-Voyce type polynomials with Euler-Seidel algorithm
5. On the Second Moment of $L (1/2, \mathrm{As} (f))$
6. Torsion groups of rational elliptic curves over $\mathbb{Z}_p$-extensions of quadratic fields: the $p\le 5$ case
7. Spectral fourth moments of Hecke--Maa{\ss} cusp forms
8. Bernoulli determinants and cuspidal subgroups
9. Generalization of Ramanujan's Continued Fractions for Even Order
10. Representability of systems of proportionally modular numerical semigroups
11. Area correlations related to lattice points in discs
12. The mean value of the digits of $1/p$
13. Exact classification of elliptic curves $y^{2}=x^{3}-pqx$ with rank $0$ and trivial $\Sha[2]$
14. Strongly complete sets and a conjecture of Erd\H{o}s
15. An asymptotic Sidon basis of order $3-\eta$
16. Heat Kernel and Closed Geodesic Asymptotics for Nilpotent Coverings
17. Resurgent Lambert series from Feynman and beyond

arXiv math.NTの新着論文13本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-15/

1. A few remarks on the Baez-Duarte Criterion
2. Solomon zeta functions over arithmetic orders
3. Curious identities involving Legendre polynomials and Ap\'ery-like numbers
4. Odd Parts of Derivative Period Polynomials and a Logarithmic Transition Scale
5. Local statistics and average rank of genus $g$ hyperelliptic curves with a Weierstrass point
6. On lower bounds for canonical heights of the map $\phi(X,Y)=(Y,X+Y^D+b)$
7. Euler systems and the symmetric square of a Hida family
8. Cyclic Projective Orbits on Rational Normal Curves and MDS Codes
9. A Note on Iterated Beatty Sequences
10. Ranks of Elliptic Curves Twisted by Quadratic Forms
11. $p$-adic Sum-Product, Projections, and Furstenberg Sets
12. Genus and Gonality of Small Curves, Dynamical Uniform Boundedness, and Bifurcation
13. A universal leading-residue formula for Witten zeta functions

arXiv math.NTの新着論文46本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-14/

1. A counterexample to a subadditivity conjecture of Cohen for Sophie Germain cyclic numbers
2. Affine monodromy and exact value distributions over finite fields
3. Hyperbolic Arcsine Kernels, Finite Fourier Filters, and Quartic Central Binomial Harmonic Sums
4. Integer Sequences which Are Closed with Respect to Multiplication and whose Sumset does not Intersect the Sequence
5. Simultaneous popular polynomial differences over finite fields
6. On the Summatory Function of $d_3(n)$
7. Local monodromy of unit root F-isocrystals from Shimura varieties
8. A resolution of Kellner's conjectures on Wilson quotients
9. On a Class of Hypergeometric Sums via Recurrences and Product Binomial-Harmonic Identities
10. Class Number Relations in Abelian Extensions of Global Fields
11. Long Intervals Without Distinct Multiples of the First $n$ Positive Integers
12. Orbit Transversality for Abelian Varieties
13. Sign Patterns in a Two Colored Partition Companion series
14. The Prime Digit Distribution Conjecture: A Formal Proof of Average Digit Equidistribution in the Prime Numbers
15. Greenberg's $\mu=0$ conjecture for lisse sheaves over global function fields
16. The rank of the modular multiplication matrix
17. Weak Inhomogeneous Poissonian Pair Correlation and Equidistribution
18. Sums of Kloosterman sums formed with modular symbols
19. Kloosterman sign changes with moduli having at most five prime factors
20. Positivity and tails of Jacobi theta series
21. Lattice point counting in Cygan--Kor\'anyi balls on Heisenberg groups
22. Disproofs of two conjectures concerning nondeficient numbers
23. Exact Frequencies of Consecutive Quadratic Residue and Nonresidue Patterns Modulo a Prime
24. Higher-Order Congruence for Reciprocal Power Sums and Generalized Lehmer-Type Products
25. On Small Doubling in Right-Ordered Groups and Baumslag-Solitar Groups-II
26. Unexpected primes of good reduction in quotients of modular and Shimura curves
27. p-adic Properties of Translated Division Polynomials and Somos Sequences
28. Two local zero-sum problems
29. Superlinear complexity of the $(3/2)^n$ steering word
30. Local-global compatibility of automorphic Galois representations over CM fields at $p$
31. Adjoint Bloch--Kato Selmer groups of regular algebraic automorphic Galois representations
32. A decomposition of Weyl group multiple Dirichlet series for symmetrizable Kac-Moody root systems
33. The Ramanujan Challenge For AI
34. On the Canonical Height Gap for Polynomial Maps and Portraits of Preperiodic Points of Polynomials with Height $0$
35. Bump-Friedberg type periods beyond the cuspidal spectrum
36. Combinatorial identities derived from explicit formulas of Gauss hypergeometric functions
37. The Aubert and Bernstein involutions for disconnected groups
38. The Arithmetic of Semirings Part I: Ideals
39. Zero-one laws for uniform approximation via Gaussian and Eisenstein integers
40. A dual linear programming bound for sphere packing in dimension 36
41. Intrinsic ergodicity for $\mathfrak{B}$-free integers in number fields
42. The combinatorics of sector renormalization
43. Arithmetic Properties for $k$-Color Analogue of Simultaneously $s$-Regular and $t$-Distinct Partitions
44. Fractal uncertainty principle over $\mathbb{Q}_p$
45. Submultiplicative Polynomials in Combinatorics
46. Exact Cardinality And Nonredundant Parametrization Of Character-Polynomial Codes

arXiv math.NTの新着論文13本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-13/

1. Joint level-weight murmurations for holomorphic newforms
2. Moments of the number of representations as sums of two prime squares
3. Remarks on a theorem of Silverman
4. The complete cubic Walsh spectrum of a permutation-inverse Boolean family
5. First Moment of derivatives of $L$-functions in a nonlinear family
6. Extension of the Equation $\sum\limits_{j=1}^{k}jF_{j}^{p}=F_{n}^{q}$ to a Family of Lucas Sequences
7. Averages of diagonal Elliott-Halberstam problem twisted by M\"obius function with Sobolev and H\"older-Zygmund weights
8. The Young Tableaux Hopf algebra and multiple Schur series
9. Asymptotic Formula for Multipartitions
10. Chevalley-Herbrand formulas and Z p -extensions of a p-principal imaginary quadratic field
11. Hankel determinants of weighted binary sums of digits
12. Counting odd genus $2$ curves with a marked rational $3$-torsion point
13. Explicit height bounds for G-functions and unlikely intersections with lines in tori

arXiv math.NTの新着論文19本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-10/

1. Infinite families of Diophantine quadruples in $\mathbb{Z}[\sqrt{-2}]$ in the remaining exceptional congruence classes
2. Non-orthogonality of the cubic and quartic large sieves via Rankin-Selberg
3. Elliptic curves, Fourier ratio, and sampling complexity
4. On an inhomogeneous uniform Littlewood type problem
5. $L^{\infty}$-norm bounds for Siegel--Jacobi cusp forms
6. On a parametric congruence concerning generalized central trinomial coefficients
7. Explicit estimates of the weighted sum $S(x)=\sum_{n \leq x} (-2)^{\Omega(n)} \log\bigl(\frac{x}{n}\bigr).$
8. Explicit upper and lower bounds on certain functions related to $\zeta(s)$ for $s>1$
9. Proof of a conjecture of Andrews and El Bachraoui on the parity of two-color partitions
10. Rademacher-type formula and higher order Tur\'{a}n inequalities for $\ell$-regular overpartitions
11. Modular Nahm Sums for the Inverse Cartan Matrix of Type $D_r$
12. Reduction modulo p of crystalline Galois representations via {\mu}_p-equivariance
13. A Matrix Analogue of Rational Number Systems
14. Waring Problem for matrices over finite local rings
15. Modular Constructions of g-Golomb Rulers
16. Functional Limit Theorems for Random Least Common Multiples
17. Dilated Hankel determinants
18. High-degree cohomology of congruence subgroups of $\text{SL}_n(\mathcal{O})$ via cohomology of $S$-arithmetic groups
19. Sandpile groups of random bipartite graphs and families of distributions with the same moments

arXiv math.NTの新着論文26本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-09/

1. A problem of D. H. Lehmer in short intervals. II
2. Continued Fractions of Polynomial Type: Theory and Encyclopedic Dictionary
3. Four squares from three real polynomials
4. Normal numbers in sparse Cantor sets
5. Schwarz maps for modular curves
6. $p$-adic Hahn series with sparse support
7. Mordell Curves with Ordinates in Arithmetic Progression
8. Global geometrization of local smooth integral models in the Hitchin fibration for $\mathrm{GL}_n$: The Bass case
9. Ideal class monoids of cubic orders
10. Analytic proofs of Andrews-Bachraoui identities related to two-color partitions with evens in one color
11. A proof of Andrews-El Bachraoui's conjecture on the parity of coefficients of a $q$-series
12. Some Comments on Regular Overpartitions modulo $2^k$
13. Extending Recent Arithmetic Properties of Overcubic Partition Tuples
14. On capitulations of even $K$-groups and pseudo-null submodules in $\mathbb{Z}_p^d$-extensions
15. On dynamical irreducible set of polynomials
16. $p$-adic Maass--Shimura operators on $\mu$-ordinary Igusa varieties
17. A higher Gross-Zagier type formula for moduli of shtukas at deeper level
18. Reduction Types of Genus 2 Curves
19. Practical Computations of the Mertens Function: $M(10^{24})$ and $M(10^{25})$
20. A curious congruence modulo primes
21. The $abc$ Conjecture Revisited
22. A problem of D. H. Lehmer in short intervals. I
23. Covers of Bruhat-Tits trees
24. Universality for cokernels of partially random integral matrices
25. Multiplication Beyond Groups: Stratified Fourier Mechanisms in Transformer Circuits
26. Small Matrices with Large Inverses: Unimodular $4 \times 4$ Cases

arXiv math.NTの新着論文19本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-08/

1. A weaker but simpler sieve inequality
2. Integer values of $\tan(\arctan 1+\arctan 2+\cdots+\arctan n)$ are rare
3. An Explicit Expression for MZVs in Terms of Symmetric MZVs
4. Large Sets of Integers with No Harmonic Triples
5. Correlations of zeros of a family of $L$-functions in function fields with symplectic symmetry
6. Small sums of roots of unity
7. An improved upper bound on the Ruzsa number
8. On exotic Diophantine triples in $\mathbb{R}[X]$
9. Steady-State and Transient Heat Conduction Analysis Using a Polygonal Cell-Based Smoothed Finite Element Method
10. The Siegel-Weil formula in geometry and arithmetic
11. Random Multiplicative Functions and Making Squares from Polynomial Values
12. A Conditional Refinement of Page's Theorem on zeros of Dirichlet $L$-functions
13. A refined Malle conjecture for Heisenberg groups
14. A Variation Norm Carleson Theorem Along the Primes
15. Degenerations of flat connections on Riemann surfaces
16. The Euler Ensemble as a Turbulent Attractor: Parity Sectors, Zero Modes, and a Zeta Edge
17. Generalisation of Baker's Forcing Method to Arbitrary Prime and NP-hardness of Several $p$-adic Optimisations
18. Closed geodesics in homology classes on random hyperbolic surfaces of large genus
19. A generalised cross-ratio and limits of local heights