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 $p$

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/2026-06-24/

1. A Local-Global Study of Obstructed Deformation Problems II
2. A Regularised Wallis Hierarchy
3. On Zeckendorf-Niven numbers and arithmetic progressions
4. Elements in $K_4$ and regulator maps of Fermat curves
5. Zeta-regularization and natural boundaries: Sums and products of integers and primes
6. Both $AA$ and $(A+1)(A+1)$ can be small
7. An aperiodic set of Wang tiles for every quadratic irrational
8. A new attack to RSA with small private exponent and partial information
9. The Sylow Divisor Condition: a Resolution of Erd\H{o}s Problem 768
10. Holes in Valid-Extension Sets of Finite Gilbreath Sequences
11. N-ary groups of panmagic permutations from the Post coset theorem
12. The Goncharov Lie coalgebra of a field
13. Tractability versus curse of dimensionality for geometric $L_p$-discrepancies
14. Bialgebraic geometry of B\"ottcher coordinates

arXiv math.NTの新着論文33本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-23/

1. Unbounded Oscillation of Euler-Gompertz Diophantine Errors from Bell and Gould Numbers
2. Differential Addition on Twisted Edwards Curves
3. Differential addition on Jacobi quartic Curves
4. Computing the Greatest Common Divisor of Binomial Coefficients $\binom{mn}{mk}$
5. Duke for Drinfeld
6. On Bounds of Extension Degrees for Similarity of Integral Matrices over Number Fields
7. Congruences for Overcubic Partition $k$-Tuples
8. Isogeny graphs associated to Moret-Bailly families of supersingular abelian surfaces
9. On the modularity of the odd rank generating functions
10. Weighted sum formulas for finite multiple mixed values
11. Geometry of $\mathbf{F}_1$ and Cuntz-Krieger algebras
12. The ratio spectrum of Lagrange constants under linear fractional transformations
13. On finiteness properties of the unramified Iwasawa module of a $\mathbb{Z}_p$-extension with restricted ramification
14. Eichler-Selberg relations for the third-order mock theta functions
15. A Proof of a Conjecture of Zhi-Wei Sun on a Truncated Legendre-Symbol Determinant
16. Level Totients for Integer Mosaics
17. Faster enumeration of primes
18. A Greatest Common Divisor Criterion of Certain Binomial Coefficients
19. A first-exit proof of Cusick's sum-of-digits conjecture
20. The Brocard Problem: Structural Invariants, p-Adic Density, and the Generative Sieve
21. Prime-Power Rarefaction and a Density-One Lower Bound for Erd\H{o}s Problem 400
22. Rank Amplification for Shifted Equal Values of Euler's Totient Function
23. On Braverman-Kazhdan's asymptotic Hecke algebra for inner forms of $\mathrm{GL}_n$
24. Global Extrema of the Zeta Regularized Determinant on Orthogonal Flat Tori
25. Bounded elementary generation of SL_2: nearly the end
26. Panmagic permutations and N-ary groups
27. Ogus's conjecture on F-isocrystals
28. A bilinear approach to the finite field restriction problem, II
29. Bianchi groups and automorphisms of rank-four $K3$ surfaces
30. The natural extension of the $(-\beta)$-transformation
31. Betti-Whittaker periods of the contragredient representations for $\textrm{GL}(n)$
32. Codimensions one and two cohomology of Hecke congruence subgroups
33. How Stark units enter SIC overlaps

arXiv math.NTの新着論文9本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-19/

1. Randomly piercing algebraic sets
2. Consecutive integers free of certain prime factors
3. A note on equidistribution on a product of Shimura curves and Andr\'e--Oort
4. Symmetric square $L$-functions on $\mathrm{GL}_3$
5. Maximal Arboreal Galois Images for Polynomials of Twisted Carlitz Type
6. On the asymptotic density of the ordered pairs $(a,b)$ of positive integers such that $\gcd(ab,a+b)=\gcd(a,b)$
7. Four-digit Kaprekar dynamics in odd bases
8. Generating Function of single-centered Black Hole Index in CHL Models
9. Explicit descriptions of the subfields $(NL)^{pi}$ and $(NL)^{pi}(NL)^{sep}$ of $NL$ and new explicit criteria for $NL = (NL)^{pi}(NL)^{sep}$

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/2026-06-18/

1. On the Diophantine Inequality $\lvert x^{2} - 2^{a}\cdot 3^{b}\rvert < 3\max\{a,b\}$
2. Factorizations of linearized polynomials and extremal curves in odd characteristic
3. Modular Heights of Unitary Shimura Varieties II: Arithmetic Generating Series of Divisors
4. Structured lattices and their applications to security
5. Schneider--Teitelbaum Duality over a Non-spherically Complete Field
6. Explicit constructions for Ramanujan-type congruences
7. Small values of Carmichael's lambda function
8. Modular Heights of Unitary Shimura Varieties III: Proof of the Main Theorem
9. Generalization of Selberg's $3/16$ theorem for geometrically finite thin subgroups of $\operatorname{SO}(n, 1)$
10. Cram\'er-Type Moderate Deviations for Engel's Series via a Martingale Approach
11. Secretary Problem Thresholds and Convergents of $1/e$

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/2026-06-17/

1. Tail Criteria, No-Go Audits, and Ap\'ery-Type Certificate Obstructions for the Irrationality of e+\pi
2. Arithmetic Properties Satisfied by a Recent Integer Partition Function of Dombos
3. A combinatorial large sieve for Sidon sets, distances, and norm forms
4. Computing Hyperfibonacci Numbers by Means of Matrix Transformations and Jordan Forms
5. Square-Annular Dynamics and Coalescence Frontiers for $n+\tau(n)$
6. An Average-Order Theorem for a Shifted Pairwise-Coprime Extremal Problem
7. Restricted partition functions and additive complements
8. Recursions for Mock Theta Functions
9. On zero-sum problems of two new types
10. Analytic theories around the simplest screw
11. The greedy 3-sumfree sequence $S_{1,g,g+1}$
12. Spectral interpretation of Riemann zeta zeros
13. Spectral Intertwining Operators
14. Single-valued polylogarithms for higher genera
15. Perturbed Polynomial Powers and Bourgain Entropy Obstructions for Khintchin Averages

arXiv math.NTの新着論文32本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-16/

1. Atoms in the Semigroup of Non-Negative Integer Matrices
2. Power and rank-weighted sums in dense finite Sidon sets
3. Rational 2-Cycles for $x^3+bx+a$ and the Elliptic Family $Y^2=X^3+4X^2+16t^2$
4. Every natural number is a sum of distinct semiprime unit fractions
5. On concatenations of two $k$-generalized Pell numbers
6. Counting Algebraic Integers of Bounded Height in Cyclotomic Fields
7. A full $p^{4r}$ supercongruence tower for a level-three symmetric-cube hypergeometric sequence
8. Large values of quadratic Dirichlet $L$-functions of prime-related moduli
9. The Bateman-Horn conjecture on average for generalized von Mangoldt Functions
10. A Beyond Endoscopy Derivation of the Functional Equation for the Symmetric-Square L-Function
11. Square-root cancellation for sums of coefficients of $\operatorname{GL}(m)$-automorphic forms over values of random polynomials
12. A parametric family of primes p = km(m+1) + e + 2kq: heuristic laws, conditional theorems, and unconditional primality certificates
13. On periodic sign changes for weighted representations of integers as colored sums of triangular and generalized pentagonal numbers
14. Thakur's hypotheses on power sums of $\mathbb{F}_q[t]$
15. Indivisibility of ray class groups of real quadratic fields
16. Two $q$-congruences from Jackson's ${}_8\phi_7$ summation and Andrews' ${}_4\phi_3$ summation
17. The difference of the sums of odd and even parts of restricted partitions
18. Obstructions and kernel transport for Hecke lifts of partition q-brackets
19. Divided differences and complex variations of multiple zeta-star values
20. Generalized Bell polynomial operators arising from generalized normal ordering
21. Quantitative Oppenheim Conjecture for Random Quadratic Forms and Optimal Variance Bounds in Function Fields
22. A counterexample to the near-quadratic Elekes--R\'onyai expander conjecture over $\mathbb R$
23. Footnote to a theorem of Phagan on actions of a cyclic group
24. On the classification of indecomposable Ekedahl-Oort strata in unitary Shimura varieties, and related Newton polygons
25. Transformers Learn the Mestre-Nagao Heuristic
26. The distribution of the de Moivre experiment
27. Dominant Zeros of Nekrasov--Okounkov Polynomials
28. Dual Affine Spiral Orbits on $\mathbb{Z}^2$ Generated by Paired Unit Squares
29. Non-Archimedean balanced metrics and their application to totally degenerate abelian varieties
30. Torsors of Generalized del Pezzo Tori and Brauer Groups
31. An Asymmetric Formula for Interval Consonance and its Relation to Harmonic Coincidence
32. The Grothendieck-Katz Conjecture for privileged local systems

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/2026-06-15/

1. On $U_p$-congruences for meromorphic modular forms with supersingularity
2. Secondary terms for first moments of Selmer groups of twists of elliptic curves over global function fields
3. Residue Restrictions for a Two-Color Partition Series
4. Almost perfect inhomogeneous powers in arithmetic progression
5. Counting the number of $1_{n}$-preperiodic integral points of a discrete dynamical system with applications from arithmetic statistics, VII
6. A Weil Sum Approach to Permutation Polynomials over Quadratic Extensions of Finite Fields
7. Sum of parts in overpartitions and partitions without repeated odd parts
8. Semistable reduction of smooth quartics
9. Explicit local stable resolution of cusps
10. Validated numerics for the Gauss problem on continued fractions
11. Adelic line bundles over a N\'eron model

arXiv math.NTの新着論文12本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-12/

1. Lower bounds on expressions depending on the functions {\boldmath$\varphi(n)$}, {\boldmath$\psi(n)$} and {\boldmath$\sigma(n)$}, III
2. Root Clusters and Multiclusters over Imperfect Hilbertian Fields
3. An AI Proof of 18-Variable Undecidability for Diophantine Equations over $\mathbb Z[i]$
4. Splitting of Polynomial Families via Galois Theory
5. Effective Estimates for a Class of Farey Fraction Sums and Bounds for Mundici-Type Constants
6. Multi-target hyperbolic sieves and elliptic trace obstructions
7. Ramanujan's and Lim's Identities and Harmonic Maass--Jacobi Forms
8. Discrete Fourier Transform Approach to Cyclically Covering Subspaces of $\mathbb{F}^n_q$
9. Some new modular Nahm sums of ranks 3 and 4
10. Split primes and the Elekes-R\'onyai problem
11. Trace spectra of simplices in large sets
12. Sphere Packings in Higher Dimension (after Boaz Klartag)

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/2026-06-11/

1. Rankin--Selberg Subconvexity via Spectral Reciprocity
2. Multivariate Period Rings
3. The p-adic Cauchy Theorem and Overconvergent Period Sheaves
4. Proofs of two $q$-congruence conjectures of Guo
5. Modular variants of p-adic fundamental sequence
6. Capparelli's partition theorem as part of an infinite hierarchy: Combinatorial and Weighted Words extensions of recent work
7. A note on a conjecture of Ng
8. Answer to a decomposition question on tori raised by Colliot-Th\'el\`ene and Sansuc
9. Beating Product Constructions for Linear Equations Over Finite Fields
10. On Perfectoidizaiton of Finite Algebras over a Perfectoid Ring
11. Moduli of Supersingular Abelian Varieties in Dimensions $g\leq 5$