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