プレプリどんどん: math.NT

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