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

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/2026-05-27/

1. A note on uniform version of Littlewood inequality and Fibonacci numbers
2. On planar functions over $\mathbb{F}_{q^3}$
3. Problems in additive number theory, VII: The structure of additive $h$-bases for $n$
4. Connected components of the ranges of twisted divisor functions on number fields
5. Notes on congruence zeta functions via a Berkovich approach
6. Towards a generalized Maeda conjecture for modular forms with quadratic nebentypus
7. Saturation and No-Go Theorems for Scalar Poisson Certificates of Gaussian Mass Maximality
8. Lower bounds for the Hausdorff dimension of expressible sets
9. Ultra Kolyvagin systems and higher Fitting ideals of Iwasawa Selmer groups
10. Words for generalized Markov numbers
11. Products involving the real parts of Jacobi sums and related cyclotomic matrices
12. Ekedahl-Oort strata under natural embeddings of orthogonal and unitary Shimura varieties
13. The Northcott Property for Composites of Number Fields of Bounded Degree
14. Inhomogeneous Approximation by Sums of Roots
15. The V/L recursion for Macdonald's 7th Variation Schur polynomials
16. Prime Certificates for Exact Vertex-Coprime Ramsey Numbers
17. Rank-two recurrence results for polynomials and questions of dynamical Mordell--Lang type
18. A Continuum of Small-cap Decouplings and Exponential Sums for the Moment Curve in $\mathbb{R}^4$
19. Structural properties and tilting correspondences of perfectoid towers

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/2026-05-26/

1. On some arithmetic conditions of recurrent sequences modulo prime p
2. On the Harris-Viehmann conjecture for Hodge-Newton reducible local Shimura data of abelian type
3. On the binary digits of the Erd\H{o}s-Borwein constant
4. The $\theta = \infty$ Conjecture and the Riemann Hypothesis for Automorphic $L$-functions
5. Counting Rational Points on Danielewski and Double Danielewski Surfaces over Finite Fields
6. Tribonacci properties of identities, matrices, and determinants
7. Valuation Separation for Coprime Lucas Products
8. Equality in a Reverse Minkowski Shell Bound for Integral Lattices via Spherical Designs
9. Simultaneous Periods for Families of Rational Maps Modulo Primes
10. Hilbert-90 quotient maps, torsion defects, and symmetric monodromy
11. Lubin-Tate representations over nontrivial finite Galois extensions of $\mathbb{Q}_{p}$ are not Aut-intrinsically Hodge-Tate
12. Variational estimate for the family of discrete averages associated to simplices
13. The Frobenius problem for shifted square sequences starting with a multiple of 4
14. A Note on Abelian Monogenic Trinomials
15. Incidence Obstructions for Power Products in Elliptic Divisibility Sequences
16. Banded quadratic digit functions along irreducible polynomials over finite fields
17. A proof of the $4,7$ cases of Sylvester's conjecture on cube sums
18. Boundary CM points and class groups of small exponent
19. Orbit decomposition statistics for discrete dynamical systems: the Ces\`aro mean and a large deviation principle
20. On the Maximality, Weierstrass Semigroups, and Automorphism Group of the Curve $Y^{q+1} = X^n(X^n + 1)$
21. The $\Delta$ property: a bridge between split graphs and Number Theory
22. Lattice point counting problems on step-two nilpotent Lie groups

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/2026-05-25/

1. The Poisson Tail Conjecture for Primes in Short Intervals
2. Cullen and Woodall numbers in Padovan and Perrin sequences
3. Distributions of Iwasawa $\lambda$-invariants of $\mathbf{Z}_p$-towers over supersingular isogeny graphs
4. On modular forms of rational weight satisfying the canonical second-order linear modular differential equation
5. Congruence Classes of Supporting the Erd\"{o}s-Straus Conjecture I: Tame Solutions
6. Computing Gamma(p/q) with Beta function values
7. Concise and elegant proofs of three formulas for complete Bell polynomials
8. Sets of large values of polynomial multi-correlation functions
9. Definability via the tilting correspondence
10. Top-dimensional rational cohomology of the congruence subgroup $\Gamma_{0,n}^+(p)$
11. Balanced intersection size distributions in projective planes

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/2026-05-22/

1. On the Natural Density of Monic Integer Polynomials with Roots in a Fixed Number Field
2. Port Fillings for Primary Pseudoperfect Numbers
3. A generalization of the Erd\H{o}s-Sierpi\'nski conjecture
4. A Matrix-Theoretic Exact Formula for Counting Primes in Intervals Between Consecutive Odd Squares
5. 2007: An Arboreal Odyssey: A View of Arboreal Galois Representations and Applications, from Early in the Subject's History
6. Escaping Chaos in Random Multiplicative Functions
7. Rational dynamics of a prime-representing map
8. The reverse Goldbach problem and a refined Zsiflaw--Legeis theorem
9. Coset-refined trace statistics, nodal characters, and affine branches in cubic norm tori
10. A Uniform Random-Lattice Tail Bound for the SVP Kissing-Profile Parameter
11. On the structure of fine Mordell-Weil groups over a $\mathbb{Z}_p$-extension and its intermediate subextensions
12. The distribution of semi-integral points on a class of singular cubic hypersurfaces
13. A quick distributional way to reproduce some results of the Riemann zeta function
14. A Complete Characterization of Heron Triangles with Two Perfect Square Sides and the All-Square Equivalence Condition
15. Arboreal Galois Groups of a PCF Map with Strictly Pre-periodic Critical Points
16. Rethinking the work of Langlands on Eisenstein series
17. Lines in the prime number graph
18. Bell Transforms of Arithmetic Functions: Euler Products, Congruences, and Polynomial Sequences
19. Bases of associated Galois modules in general wildly ramified extensions and in elementary abelian extensions of degree $p^2$
20. From Hilbert's Tenth Problem to Quantum Speedup: Explicit Oracles for Bounded Diophantine Systems
21. Graphs from quadratic forms and vector spaces over finite fields
22. Closed geodesics in short intervals for random hyperbolic surfaces

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/2026-05-21/

1. High-Precision Approximation of Riemann Zeros via the Truncated Weil Form
2. Eigenvalue Distribution of $p$-adic Random Matrices Among Algebraic Extensions, with an Analogue for $p$-adic Random Polynomials
3. Bounded-box reductions in the Subbarao-Warren problem for unitary perfect numbers
4. On discrepancy estimates for pseudorandom vectors constructed by the elliptic curve congruential generator
5. Limiting Distribution and Rate of Convergence for GL(3) Fourier Coefficients
6. Beyond endoscopy for $\mathsf{GL}_2$ over $\mathbb{Q}$ with ramification 4: contribution of non-elliptic parts
7. Generalized Fermat equation over cyclotomic $\mathbb{Z}_l$-extensions of totally real fields
8. Precise Asymptotics and Exact Formulas for Tensor Product Energies of Fibonacci Lattices
9. A Local Valuation Criterion for Quadratic-Permutation Interleaved Zadoff--Chu Sequences
10. Quasiautomorphic forms are isomorphic to vector-valued automorphic forms
11. On a conjecture of Amdeberhan, Andrews and Ballantine for double Lambert series
12. Binomial coefficients with divisors avoiding an interval
13. An Improved Upper Bound for the Dirichlet Spectrum in Diophantine Approximation
14. Arithmetic Properties of Overcolored Odd Partitions
15. Sharp omega results for the divisor and circle problems
16. Manin's conjecture for semi-integral curves and $\mathbb A^1$-connectedness
17. Measuring Decidability as Related to Busy Beaver Numbers
18. Extensionalism without Logicism: Ambrose and Extensional Logic
19. An explicit lower bound for the unit distance problem
20. The pro-\'etale fundamental group of singular schemes
21. Remarks on the disproof of the unit distance conjecture
22. A strange continued fraction associated with the Romik map

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/2026-05-20/

1. The generalized Montgomery-Hooley formula: A survey
2. Short Salem polynomials
3. Fibonacci Numbers and Vieta Jumping for a Rational Diophantine Equation
4. Hal\'asz theorems for Gaussian ideals in sectors and short intervals
5. On nonconvex constellations among primes II: (458,3240)
6. A formula of counting divisors in integers rings: a generalization of the divisor function $d_0(n)$
7. On optimal $p$-adic uniformization of unitary Shimura curves
8. A Determinant Congruence Conjectured by Sun
9. Sun-type determinant and permanent congruences
10. Two determinant evaluations in Sun's conjectures involving Legendre symbols
11. On the Goldbach problem with restricted primes
12. The inhomogeneous Khintchine Theorem in dimension two
13. Split-prime supercongruence at the mixed CM point (1/6, 1/3; 1)
14. A Fourier-Free Density-Increment Proof of Roth's Theorem
15. Motivic Galois theory for one-loop Feynman integrals in momentum space