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/2026-06-10/

1. On partial T-adic exponential sums and partial exponential sums with p-power conductor
2. A generic categorical local Langlands correspondence for quasi-split reductive groups
3. A Tsang-range high-moment bound for $\operatorname{Im}\log L(\tfrac12+it,\chi)$ under GRH
4. Prime Quadruplets and Jump Conditions on Arithmetic Functions
5. Unique decomposition of orders
6. On the Ekedahl sieve for the singular locus of the discriminant polynomial
7. Hilbert irreducibility for algebraic points
8. Eisenstein-Kronecker classes on Hilbert moduli spaces and a new construction of Katz's $p$-adic measure
9. Linear relations of four conjugates of an algebraic number of degree eight
10. A Divisor Parametrization for the Erd\H{o}s--Straus Conjecture
11. Weighted partitions with interval restrictions: exact formulas and a bivariate master identity
12. Adjacent comparison bounds and extremal sets for Ruzsa numbers
13. A natural e\~ne product construction of the Big Witt ring
14. Maximal Transcendentality of the Double-Scaled PCM
15. Ind-Banach approach to Grothendieck duality in Rigid-analytic geometry
16. On superspecial hyperelliptic curves of Rosenhain forms
17. The convergent stack
18. On the rank of hypergeometric sheaves on higher dimensional tori

arXiv math.NTの新着論文39本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-09/

1. Arithmetic Symmetry in Ideal Prouhet-Tarry-Escott Solutions
2. Explicit bounds for Dickman's function
3. Weighted Recursions for the Smallest Parts Function
4. Minkowski shapes of pure number fields
5. On the sequence $\mathrm{gcd}(a^n-1,b^n-1)$
6. Monogenity of Fibonacci polynomials and Lucas polynomials
7. A criterion for weighted uniform distribution along functions from a Hardy field
8. Gcd-closed sets and divisibility among power LCM matrices
9. $P$-adic $L$-functions: $t$-modules and Dirichlet-Goss $L$-series
10. Waring's problem involving D.H. Lehmer numbers
11. Arithmetic exceptionality of generalized Chebyshev polynomials of the second kind
12. Erd\H{o}s Problem 684 at Density One: Small-prime Parts of Binomial Coefficients and Gaussian Fluctuations
13. Murmurations in the Depth Aspect for Maass and Modular Forms
14. On special perfect polynomials over $\mathbb{F}_2$
15. Uncertainty Principles for the Number Theoretic Transform
16. A convexity proof of Pohst's inequality
17. On the degree-$2$ Siegel theta series of extremal even unimodular lattices of ranks $48$, $72$, $96$, and $120$
18. Extremal Type II lattices of rank $72$ are generated by their second shell
19. Transcendence of simple geodesics on finite modular covers
20. Zeta functions over curves
21. The Dirichlet spectrum with respect to $L_1$ norm is $\left[\frac12,1\right]$
22. Polynomial Corners Over finite Fields
23. Degenerate generalized Stirling operators of the first kind arising from generalized Heisenberg algebra
24. Weil's quadratic form via the screw function
25. Fourier Coefficients of Siegel--Eisenstein Series of Degree $2m$ and Weight $m+1$
26. Insufficiency of the algebraic Brauer--Manin obstruction for homogeneous spaces
27. Abelian surfaces of small conductor from genus 3 double covers
28. Multiple zeta values ending with a fixed string
29. On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials
30. Fine-scale statistics for $\mathbb{Q}^n$
31. Power Integral Bases in Polynomial Compositions
32. A note on large values of Dirichlet $L$-functions for characters of fixed order at $1/2<\sigma\leq 1$
33. On the Vinberg Family of K3 Surfaces
34. Covering $\mathbb{F}_2^n$ with Hamming Balls
35. Birkhoff genericity on affine subspaces in horospheres
36. Digit Mixing under Polynomial Maps
37. Restriction estimates for toral eigenfunctions and lattice points in spherical regions
38. Algebraic Hodge generic points are dense
39. Bertini theorems for Hilbert-Samuel multiplicity over finite fields

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/2026-06-08/

1. Vanishing Coefficients in Products of Quintuple Products
2. Tamagawa number formula for Jacobians
3. A mod $p$ determinant criterion for Cohen--Lenstra convergence of random $p$-adic matrices with prescribed zero patterns
4. Note on the Equivalence of Costas Polynomials and Orthomorphisms
5. Multi-scale properties of continued fraction sets
6. Connection between the Riemann zeta-function and random matrices via hyperfunctions
7. On the factorizations of integers via division algorithms for polynomials
8. Twisted Moments of Rankin-Selberg $L$-functions in the Prime-Power Level Aspect
9. Exact output statistics of Icart's encoding in the exceptional \(j=0\) case
10. Gaps in Multiplicative Sidon Sets II
11. Erd\H{o}s-Kac theorems for discriminants of number fields
12. On the Absolute Geometry of $\operatorname{Spec}\mathbf{Z}$
13. On periods and Jacobians of Heisenberg curves

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/2026-06-05/

1. Corrigendum to "Isomorphism classes of Drinfeld modules over finite fields"
2. Theorem $(1+1.9)$ on the Goldbach Conjecture
3. The Case of the Second Smallest Modulus: or why we cannot be arbitrarily careless?
4. Hasse-Weil Zeta Functions Modulo a Prime
5. On explicit Fourier expansions of theta lifts to ${\rm SO}(3,n+1)$ arising from elliptic newforms of level one
6. Exotic and inverted Kloosterman sums over semisimple algebras
7. Drinfeld modules in rank 2 with CM and S-unit j-invariants
8. Arithmetic Wu Formulas and the Generalized Hecke Theorem
9. Recent Progress around Cohen-Lenstra Heuristics
10. An Elementary Analysis of the Prime Partition Function
11. A Generalization of the Amdeberhan-Andrews-Ballantine Conjecture
12. On a conjecture on Romanoff type sumsets
13. No three algebraic conjugates of degree sixteen sum to zero
14. Arithmetic statistics of isogeny Selmer groups associated to hyperelliptic curves
15. Arithmetic Kashiwara Regularity and Orbit Classification for Filtered Strongly Equivariant $\mathcal{D}^{\dagger}$-Modules
16. Higgs bundles on the Fargues-Fontaine curve
17. Two notes on valued fields
18. Decomposition Theorem for Perfectoid Rings along General Ideals
19. Stability of the smooth Casselman-Jacquet functor

arXiv math.NTの新着論文14本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-04/

1. Enumeration of modular forms for $\Gamma_1(N)$
2. Voronoi-Hankel Transforms
3. Weighted Recursions for Hurwitz Class Numbers
4. Digit frequencies and class numbers
5. An Explicit Surjectivity Threshold for Digit Sums of Primes
6. Representations of positive integers by three almost-prime squares
7. Correspondence of discrete series representations of $\mathrm{GSp}_{2n}$ and its inner form
8. Integer points close to a transcendental curve: an algorithmic approach
9. The leading constant in Malle's conjecture
10. Khintchine's Theorem for Symmetric matrices via Flows on the Space of Symplectic Lattices
11. A Note on Jacobians with Prescribed Factors
12. Primitive inhomogeneous approximation for fixed non-singular frequencies
13. Local-global conjugacy questions for affine extensions
14. Stochastically evolving ellipsoids with symmetries

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/2026-06-03/

1. A Note on Diophantine Approximation with Restricted Denominators
2. A Fibonacci theorem for Collatz trajectories via modular graph structure
3. Generalized polygonal number representations
4. Explicit generators of the space of modular forms
5. On the Schematic and Analytic Constructions of the Local Langlands Category
6. On the Argument of the Lerch, Chowla--Selberg Formula and CM Values of $\eta(\tau)$
7. Diagonal Condition in Multiplication Table of $\displaystyle {\, \mathbb{Z} [i] / (\alpha) }$
8. Planes in quadratic 4-space and associated shapes of lattices
9. Majorization and Gaussian-Mass Maximality for Construction-A Lattices from Binary Self-Dual Codes
10. The Fontaine operator at cusps of modular curves at infinite level
11. Pair correlation of $\alpha n^{\theta}$ for random $\theta$
12. A $q$-Analogue of a Supercongruence Related to Van Hamme's (B.2) Supercongruence
13. Some new results on determinants and permanents
14. A note on partitions in the image of pre$_2$
15. On maximal Dynkin friezes
16. A conjecture of Glasby, Praeger, and Unger on permutations of $S_n$
17. On $\mathbb J$-strata with Parahoric Stabilizers in Affine Deligne-Lusztig Varieties
18. Cassini's identity for k-bonacci numbers
19. An Iwasawa-type asymptotic formula for multiple $\mathbb{Z}_p$-coverings of graphs
20. On the prime field spherical restriction conjecture in four dimensions: breaking the Stein-Tomas exponent and applications
21. Complete Families of Curves in the Moduli Space of Genus g Curves
22. Half of finite abelian groups are unit groups
23. The Abel--Jacobi map over the twistor-$\mathbb{P}^1$ and real local class field theory

arXiv math.NTの新着論文36本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-02/

1. Perfect powers in the product of denominators of elliptic curves
2. On $\mathbb{Z}_2$-extensions of real quadratic fields
3. Prescribed realisation of longest runs in continued fractions
4. Polylogarithmic Analogues of Euler's Constant
5. On the $P(t)$-adic Littlewood conjecture in odd characteristics
6. Locating a shortest vector in certain $2$-dimensional lattices
7. On indecomposable elements in lattices
8. The categorical local Langlands conjecture
9. A further study of polynomial $g_{n,q}$ over finite fields
10. Topological and Diophantine properties of lattice subset projections
11. Tame Galois Groups, Linking Numbers and Mildness
12. Piatetski-Shapiro Primes in short intervals
13. Additive Rigidity for Images of Rational Points on Abelian Varieties II: The General Case
14. A Sharp Reverse Minkowski Inequality for the Gaussian Mass of Integral Unimodular Lattices Through Rank $32$
15. Sums of Apostol's M\"{o}bius functions of order $k$
16. Distinguished defining polynomials for extensions of p-adic fields
17. Geometrization of summation formulae for quadrics
18. High moments of random multiplicative functions twisted by Fourier coefficients of modular forms
19. Intrinsic Subgroups and the $\ell$-adic Galois image
20. On a problem on a generalization of Euler's totient function
21. On cyclotomic matrices related to Kloosterman sums over finite fields
22. Infinite Moments of Class Groups for Solvable Fields with a Normal Abelian Subgroup
23. Applications of a formula of Maesaka-Seki-Watanabe type for multiple harmonic $q$-sums
24. Universality of the cokernels of random $p$-adic matrices with inhomogeneously balanced columns
25. On the unit equation $\varepsilon+\delta=n$ in cubic fields
26. On periods of Elliptic curves
27. Arithmetic regularity as an alternative to transference
28. Cyclotomic factors of rational necklace functions
29. Analogues of the Lindel\"of Hypothesis for the Barnes multiple zeta function and related problems
30. Finding the complement of an elliptic curve inside a Jacobian
31. The Primes are $2$-Accessible
32. Infinitely many holes in connectedness loci for collinear affine iterated function systems
33. Non-Archimedean Massera-Schaffer-Maligranda-Pecaric-Rajic Inequality
34. Hitting Arithmetic Progressions at the Square-Root Scale
35. The 1/2-Conjecture for $q$-Binomial Coefficients with Fractional Index
36. Three-color van der Waerden numbers grow super-exponentially

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/2026-06-01/

1. Density of subsets of squarefree elements in certain Dedekind domains
2. On the density of rational lines on diagonal cubic hypersurfaces, II
3. Transcendence and measures via the refined Diophantine exponent
4. An Improvement of Konstantoulas' Density Constant
5. Perfect powers among Jacobsthal numbers
6. Integrality of Averages of Roots of Unity and Perfect Isometries
7. The Bogomolov property for $p$-supercuspidal eigenforms
8. Visible 2-torsion in the Tate-Shafarevich group of an elliptic curve
9. On the asymptotic average diameter of blocks of uniformly distributed sequences and related results
10. Moments of partition statistics, Bell polynomials and Eisenstein-type series

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/2026-05-29/

1. On Ramanujan's $q$-Continued Fractions of Order Thirty-Four and Sixty-Eight
2. Asymptotic formulas for sums of elements from a multiplicative group
3. On a conjecture of Goldmakher
4. Mersenne numbers and the doubling map
5. Weierstrass semigroups at totally ramified places of degree one on linearized function fields
6. On the power of the discriminant of a univariate polynomial as a certain determinant in positive characteristic
7. Inducing Whittaker Functions from Higher Ranks
8. The weighted large sieve through Parseval
9. Iwasawa invariants of Bertolini--Darmon Theta Elements
10. Canonical extensions of $p$-adic shtukas on toroidal compactifications of Shimura varieties
11. Bourgain's $L^2$ pointwise ergodic theorem over function fields
12. Subsequence Sums in Permutations
13. Superspecial plane quintics with large automorphism groups
14. Lift-independence problem in the $P$-adic Simpson correspondence for curves
15. A note on Azumaya algebras and one-forms

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/2026-05-28/

1. Some Remarks on $\tau$-Congruent Numbers
2. Linnik's problem for multiplicative functions
3. $Q$-difference analogue of the Stothers-Mason theorem
4. Good Integers: (T,k)-Subclasses and Applications to Galois Duality in Coding Theory
5. Mixed thresholds in the Lonely Runner Conjecture
6. Transformation Formulae and Applications for Double Lambert Series
7. Additive Diophantine Equations involving S-Units, Factorials and Ternary Recurrences with repeated root
8. Metrical theory of signed Engel expansions
9. A unified proof of conjectures on the spaces of multiple $q$-zeta values
10. On the analytic continuation of the Riemann zeta function
11. Equidistribution of CM points and RM curves
12. The sum-product conjecture is false for real numbers
13. Riemann and the logarithmic derivatives of zeta
14. Proofs of Two Positivity Conjectures of Guo
15. Brauer--Manin obstruction from failure of Kodaira vanishing in positive characteristic