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

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/2026-07-07/

1. Recovering Kodaira types from $\ell$-torsion on elliptic curves
2. $(a,a)$-Carmichael numbers and greatest common divisors of $p-a$
3. $p$-adic rigidity for $\mathrm{GSp}_4$
4. A finite Guinand-Weil dictionary and archimedean tail order for the truncated Weil quadratic form
5. A Mackey criterion for locally analytic representations
6. Beyond Endoscopy for $\mathrm{GL}_3(\mathbb{Q})$: Functional equation for the $L$-function of a cubic order
7. Refined Humbert invariants and subvarieties of $\Ac_2(\C)$: the rank 3 case
8. Lubin's conjecture for height-one $p$-adic dynamical systems
9. On S\'ark\"ozy-S\'{o}s Theorem related to representation functions
10. Derivative-Free Richelot Isogenies via Subresultants with Algebraic Certification
11. Calculating the floor of y**(1/m)
12. Ramanujan-type identities for alternating Hurwitz zeta functions
13. The discrete logarithm problem in cokernels of $\mathcal{O}_K$-matrices
14. On the inverses of permutation polynomials of the form $h(\psi(x))\varphi(x)+g(\psi(x))$ over finite fields
15. The compositional inverses of the permutation polynomials of the form $x+\gamma\operatorname{Tr}_{q}^{q^n}(H(x))$ over $\mathbb{F}_{q^n}$
16. Extreme values of the real part of the Riemann zeta function
17. A Romanoff-type theorem for $P_2$+{$a^a$: a$\ge$ 1}
18. Modular elliptic curves and hyperbolic uniformization
19. Constructing the $\mathbf{2^{2^5} + 1 = F_5}$-gon: the first step, the 641-gon
20. Anomalous Partial Quotients in the Continued Fraction of $\sqrt{\zeta(3)-S_N}$
21. Extreme values of derivatives of Dirichlet $L$-functions
22. $p$-adic multiple $L$-functions and twisted multiple Bernoulli numbers
23. A Stretched-Exponential Bound for an Erdos--Graham Unit-Fraction Problem
24. Distinctness of the generalized $n$-dimensional Kloosterman sums
25. On the number of perfect positive definite quadratic forms
26. Improving on the Brun-Titchmarsh Theorem
27. A Gaussian-Perron Smoothed Prime-Side Defect for Local Profiles Near Critical-Line Zeros of the Riemann Zeta Function
28. A proof of Riemann's hypothesis via Hadamard-Weierstrass factorization
29. Complete Asymptotic Expansion of the Additive Mertens Sum $S_k(x)$
30. Symmetric Spectral Reciprocity for $\mathrm{GL}(2)$ and Uniform Subconvexity
31. Supercongruences Arising from Truncated Appell Series
32. A decades-long breakthrough in zero-density estimates and primes in short intervals
33. Pythagorean triples in level sets of completely multiplicative functions
34. On the exterior square $\varepsilon$-factors of $GL_n$
35. Truncated Multiple Zeta Values
36. Class-Number-One Cubic Fricke Companions on $\Gamma_0(2)^+$ and an Exact Chudnovsky Bridge
37. Exceptional rational functions of degree 5 over finite fields: classification by monodromy, ramification, and the Riemann-Hurwitz formula
38. Thue equations that simultaneously fail the Hasse principle
39. Sharp Circular Sampling and Derivative Period Polynomials
40. Calculating the natural density of Mersenne numbers using nonstandard mathematical analysis
41. Iwasawa invariants of sharp/flat $2$-adic $L$-functions for quadratic twists of elliptic curves
42. An improved lower bound for odd integers not of the form $p+2^a+2^b$
43. Large $B_2[g]$ subsets of the first squares
44. Signed graphs with fixed smallest eigenvalue at least $-3$ and their lattices
45. Partitions with parity restrictions: a bijective approach
46. Dynamics of integer zeroes of homogeneous quadratic equations over $\mathbb{R}^3$
47. A Combinatorial Proof for Partitions of Pythagorean Triples Into Three Parts
48. Presenting restricted Steinberg modules of general linear groups
49. A MacMahon Analysis View of 4 Diagonal DSPPs
50. A sharp lower bound for some reciprocal Rado numbers
51. Sharpening Borel's result in Diophantine approximation
52. Theta correspondence as a C*-correspondence
53. Integer Coefficient Power Series with Prescribed Zero Sets
54. The Minkowski grid has robustly many repeated distances

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/2026-07-03/

1. Utilizing Smoothing Techniques to Bound $|\zeta(1+it)|$
2. Necessary and sufficient conditions on the order of a finite field $\mathbb{F}_q$ for the easy identification of primitive polynomials of degree 2
3. Formalized $q$-series: The Rogers-Ramanujan Identities and Beyond
4. A Pfaffian Proof and Generalization of a Conjecture of Sun Zhiwei
5. On Euclidean systems of ray classes
6. A Coordinate System for Collatz Dynamics
7. Gross-Zagier formula for the $4, 7$ cases of Sylvester's conjecture
8. On a Smoothed Walfisz Divisor Problem
9. The Eichler--Selberg trace formula for Hilbert cusp forms, the class numbers of quartic CM fields, and their distributions
10. Genuine and strongly genuine polynomials: With an application to the persistence of Galois groups under specialization
11. Iwasawa-Type Spectral Resultant Growth Laws for Grover Walks on Graph Towers
12. Algorithms for hyperelliptic Mumford Curves $p$-adic Uniformization, $p$-adic integrals and $p$-adic heights
13. The trianguline variety for reductive groups
14. Cyclic Codes and Cyclically Covering Subspaces over Finite Fields
15. Beyond the Giampietro--Darmon Conjecture
16. The Gauss periods and cyclotomic matrices involving Gauss sums over cyclic groups
17. A note on polyhedral cones and toric polylogarithms
18. The universal zero-sum invariant and weighted zero-sum for infinite abelian groups II
19. Recent progress on the geometric Bombieri--Lang conjecture
20. Black Holes and Random Variables

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/2026-07-02/

1. Finiteness for \'{E}tale Fundamental Groups of N\'{e}ron Models
2. Critical Zeros and Unconditional Mean Value Theorems for twisted $\hbox{PGL}(2)$ and $\hbox{PGL}(3)$ $\mathrm{L}$-functions
3. Functional Equations Characterize Dirichlet Characters
4. Character sums over smooth numbers
5. Depth Two Mock Modularity by Eisenstein Series Coupling
6. Rank of P\'olya Groups in Lecacheux Parametric Family of Quintic Fields
7. The Minimal Absolute Value of Sums of Fifth Roots of Unity
8. Reductions Of Crystalline Representations Of Fractional Slope $
9. Distribution of Selmer ranks in prime cyclic extensions
10. An absolute bound for generalized Diophantine tuples over polynomial rings
11. Lower bounds for low moments of character sums, I: Short sums with general multiplicative weights
12. On a conjecture of Andrews and almost alternating sign patterns
13. Central isogenies and conjugacy classes in reductive groups
14. On the Extended 1-2-3 Conjecture of Pilz
15. $A_3$-formality for pro-2 Demushkin groups
16. Sheared Witt Vectors

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/2026-07-01/

1. Power-integral matrices over number fields: the Drazin inverse, pseudo-determinant, and numerical semigroups
2. On the exponential Diophantine equation $(a^n+1)(b^n+1)=x^2$
3. Several classes of permutation pentanomials
4. Some new congruences and identities for $SOME(n)$, $DSOME(n)$, $\overline{SOME}(n)$ functions and analogues
5. On the Finiteness of Geometric Representations for Varieties over Finite Fields
6. Counting zeros of Artin $L$-functions
7. The classification of real quadratic fields which satisfy Hammarhjelm's condition
8. A cohomological translation of the Kaplansky radical for profinite groups
9. Sign Laws and Mock Theta Functions
10. Diophantine rank stability and non-vanishing of $L$-functions
11. Tamagawa ratios and unbounded Selmer moments
12. Supersingular elliptic curves and twisting endomorphisms
13. Local-global compatibility at $p\neq\ell$ for torsion automorphic forms
14. An Efficient Algorithm for Estimating Prime Counts
15. Construction of Generically Ordinary Families of Hyperelliptic Curves
16. Galois Extensions via Finiteness of Orbits
17. EKOR and BT stratifications for basic unramified $\mathrm{GU}(1,n-1)$ Rapoport-Zink spaces
18. Linear equations and chromatic thresholds in $B_h$ sets
19. A generalization of partition identities of G\"ollnitz-Gordon, Rogers-Ramanujan and Nandi

arXiv math.NTの新着論文47本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-30/

1. Classification of Boolean Cubic Forms in Ten Variables
2. On Brocard's problem with Padovan and Perrin numbers
3. Riesz Means of Quadratic Class Numbers
4. To be or not to be local
5. On Carmichael numbers of the form $2^np^m+1$
6. On the Monotonicity of Higher-Fold Representation Functions
7. Maximal Gaps for Dilated Lacunary Integer Sequences
8. An Explicit Cubic Ramanujan--Sato Series for $1/\pi$ on $\Gamma_0(2)^+$ at $D=-163$
9. Moment Estimates and Discrepancy for Sums of Square Roots Modulo One
10. Point counts of abelian varieties over finite fields determining their zeta function
11. Distribution of random multiplicative functions in short intervals, with proper normalization
12. On Dense Orbit Transversality for Endomorphisms of Abelian Varieties
13. A Resolution of Erd\H{o}s Problem 731 under Dyadic Regularity
14. Gap-Sums via Quasi-Arithmetic Means with Applications to Fibonacci and Lucas Sequences
15. The van der Corput property for sums of two squares
16. Procounting measures and the Bateman--Horn conjecture
17. A finiteness theorem for mod $p$ Galois representations over global function fields
18. Quantum models of the Riemann zeta function, lattice spin models and algebraic models of entanglement
19. Iterated extensions and the ramification dichotomy
20. For which real quadratic fields is Kim's octonary form universal?
21. Andr\'{e}'s theorem and weakly bounded height
22. The Categorical Local Langlands Correspondence and Anabelomorphy
23. Multiplicative functions additive on partitions of $2k$ nonzero squares
24. Finite-core Volterra reductions for a Weyl-positive Riemann phase kernel
25. On the level of distribution of Goldbach primes and its applications
26. Linear equations on $t$-modules
27. Double weighted sum involving $\mathrm{GL}(2)$ Fourier coefficients
28. Bessel Distributions and Kloosterman Sums
29. Mean values and variances of the digits of $1/p$
30. Harder's conjecture and Hermitian automorphic forms
31. On the diffraction spectrum of the set of visible points in lattices and certain cut-and-project sets
32. On integers of the form \(p+F_{2^k}+F_q\)
33. Structured Solutions of Prime-Base Binomial Congruences
34. Pseudodifferential Jacobi forms and Geometric Rankin-Cohen Brackets
35. Computing sieve integrals using LattE, and the density of integers with a localized divisor
36. Exact approximation order of real numbers in Cantor series expansions
37. Products of prime ideals in ray class groups
38. Moments and sign changes of symmetric power $L$-function coefficients over sums of squares
39. Shifted convolution sums of coefficients of symmetric power $L$-functions with $k$-full kernels over sums of squares in arithmetic progressions
40. Weakly Consecutive Sequences
41. Some quadratically closed fields of nimbers
42. The Thickness of Infinite Sidon Sets
43. A sharp 5/8 bound for an Erd\H{o}s-S\'os pairwise-sums problem
44. Palindromes on the $\tau$-circle: A note for Palindrome Tau Day, 6/28/26
45. Small complete 3-term progression free sets in cyclic groups and vector spaces
46. On a two-color partition series and its companions
47. From some Pisot numerations to topological groups

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/2026-06-29/

1. Sharp Bounds for Moments of the Dedekind Zeta Function
2. Cohomological Obstructions for Varieties over $p$-adic Function Fields
3. Separable integer partition classes and Slater's list -- II
4. On Franke's theorem in the simplest case
5. Large common values of generalized Ankeny-Brauer-Chowla recurrences
6. Sign law for Ramanujan's third order mock theta function $\rho(q)$
7. Transversal Difference Numbers in Finite Abelian Quotients
8. The Natural Extension for the Triangle Map (a Multi-dimensional Continued Fraction) with An Internal Symmetry from Young Conjugation
9. Perfect powers in sequences of polygonal numbers
10. Kontsevich graphs associated with specific multiple zeta values
11. Series involving parametric harmonic zeta function
12. Average divisibility in character tables of $\mathrm{GL}_2(\mathbb{F}_q)$
13. Stability of the exterior cube $\gamma$-factors for $\mathrm{GL}(6)$

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/2026-06-26/

1. Optimal homological vanishing: cancellation of character sums and Patterson's conjecture over $\mathbb{F}_q[t]$
2. Rank-Two Drinfeld Module over Elliptic Curves
3. Computating decomposition groups and inertia groups using Newton polygons
4. Deterministic and Efficient Ideal Arithmetic via Two-Element Representations
5. Averaged Fourier Estimates and Dyadic Approximation on the Cantor set
6. Adelic Line Bundles, Arithmetic Positivity and Diophantine Geometry
7. Quantitativity in the Mordell Conjecture
8. Determining Newforms via various relations among Fourier Coefficients
9. The Bogomolov Property through Galois Representations
10. A direct proof of Mono-Rolen-Stumpenhusen and new constructions via the Maass raising operators
11. Weighted Fruit Diophantine Equations and Hyperelliptic Curves
12. Amplified moments of the Riemann zeta function
13. Sharp endpoint multilinear estimates for oscillatory integrals and spectral clusters
14. Proof of Cigler's conjecture on $q$-Hoggatt numbers
15. On a conjecture by Koll\'ar and Sacc\`a
16. Cusp Excursions, Lattice Points on Manifolds, and the Mizohata-Takeuchi Conjecture
17. Inequalities among higher-order difference sets, or, remarks on a construction of Ruzsa
18. Automorphism Groups of Uniform Dessins d'Enfants of Genus at Least Two
19. On automorphisms of $\mathscr{B}$-admissible and related subshifts
20. Linear Code Conversion in the Merge Regime: General Bounds and Reed--Muller Constructions
21. On the resonant Carleson-Radon transform in all dimensions. The degree one resonant case

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/2026-06-25/

1. Cusp Volumes and Rational Points on Spheres
2. Binary Trees and Sum of Two Squares
3. Positive dyadic density for rational weighted binary expansions
4. Nonsimilar half-neighbors over fields of characteristic 2
5. Divisibility Biases in the Orders of Elliptic Curve Reductions
6. Negative discrete second moments of Dirichlet $L$-functions
7. Binomial sequences over prime fields
8. Hyperelliptic Atkin-Lehner quotients of Shimura curves
9. Stable Quadratic Polynomials over $\mathbb{Q}(i)$
10. Metric results for dyadic approximation on the middle-third Cantor set
11. Prescribed lifts of 2-dimensional representations
12. Integrality of height-one formal groups
13. Iwasawa Theory for K3 Surfaces over Finite Fields
14. Proof of the Gawron-Miska-Ulas conjecture concerning unboundedness of coefficients of power series expansion of $\prod_{n=0}^{\infty}(1-x^{2^{n}})^m$
15. Number Fields with Arbitrarily Large Minimal Index
16. A resolution of Erd\H{o}s Problem 1061 on the sum-of-divisors function
17. Proofs of four conjectural identities on modular rank four Nahm sums
18. Chebotarev geodesic theorem: split case
19. Every Nonnegative Integer Is a Sum of a Triangular, a Pentagonal, and a Heptagonal Number
20. Potential semistability of Finite height Galois representations: Relative case
21. On $k$-color mex-related partition functions
22. Extensions of maximal symplectic groups acting on the superspecial K3 surface in characteristic $p$