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/2026-03-03/

1. The minimal width of universal $p$-adic ReLU neural networks
2. Zolotarev's Magical Proof of Quadratic Reciprocity
3. Unconditional Density Bounds for Quadratic Norm-Form Energies via Lorentzian Spectral Weights
4. On log crystalline higher direct image
5. The Bombieri--van der Poorten Formula for Partial Quotients of Higher Degree Algebraic Irrationals
6. A Deterministic Fractal Set Derived from the Sequence of Prime Numbers
7. On the quadratic Waring-Goldbach problem with primes in Piatetski-Shapiro sets
8. Another proofs of Zagier's formula for multiple zeta values and Murakami's formula for multiple $t$-values
9. Almost prime numbers
10. On bilinear sums with modular square roots and applications II
11. Equidistribution in shrinking sets for arithmetic spherical harmonics
12. The 2-term Dilogarithm
13. Automatic convergence for holomorphic modular forms
14. Inequalities for the number of $t$-hooks in two partition classes arising from sum-product identities
15. Weighted averages of $p$-adic hypergeometric functions and traces of Frobenius of elliptic curves
16. Regulator Constants and Cohomology
17. On a theorem of Schmidt's subspace theory with moving targets
18. Relative integral spinor norm groups over dyadic local fields
19. The overconvergence of multivariable $(\varphi_q,\mathcal{O}_K^{\times})$-modules at the perfectoid level
20. Lower bounds for the large deviations and moments of the Riemann zeta function on the critical line
21. Jacob's ladders and the equivalent of the Fermat-Wiles theorem generated by the Hardy-Littlewood formula (1921)
22. Transfer principles and the Kato-Kuzumaki conjecture
23. Mass equidistribution for lifts on hyperbolic $4$-manifolds
24. Partial weight one modularity for Galois representations associated to mod $p$ Hilbert modular forms
25. An estimate for incomplete mixed character sums and applications
26. Torsion cycles on Fermat varieties
27. A note on the M\"obius uncertainty principle for posets
28. Proofs of some conjectures of Okazaki and Smith on line defect half-indices of ${\rm SU}(N)$ Chern-Simons theories
29. Modularity of special cycles on Shimura varieties: a survey
30. Covers of curves, Ceresa cycles, and Unlikely intersections
31. Non-Archimedean Tarski-Maligranda Inequalities
32. A lift of the colored Jones polynomial of a knot
33. Overcolored Partition Restricted by Parity of the Parts
34. A Dynamical Fekete-Szeg\H{o} Theorem
35. Berkovich $2$-motives and normed ring stacks
36. Coexact $1$-form spectral gaps of hyperbolic rational homology spheres
37. Horizontal Kakeya maximal operators in finite Heisenberg groups: Exact exponents and applications

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/2026-03-02/

1. Completeness of exponentially increasing sequences
2. Meta-automatic Sequences
3. Duffin--Schaeffer examples, real residue systems, and Bohr-set primes
4. Arithmetic properties of arguments of algebraic numbers on the unit circle
5. Counting number fields using multiple Dirichlet series
6. 4-rank distribution of Picard groups of hyperelliptic curves via $C$-symmetric matrices
7. On quasi-split orthogonal local models of PEL type D
8. Products of factorials which are products of factorials
9. A Functorial Refinement of the Franke Filtration and the Jacquet--Langlands Correspondence for Spaces of Automorphic Forms
10. Improved, sublinear projective Schwartz-Zippel and (sub)quadratic dimension growth bounds in arbitrary codimension
11. Periods of hyperplane arrangements and multiple polylogarithms
12. Newton strata realization for hypersurfaces via explicit p-adic cohomology
13. Diamond Determinants and Somos Sequences
14. On Weierstrass semigroups of maximal Fermat function fields
15. Sarnak's Program for Erd\H{o}s Sieves. Part I: Topological Dynamics and Light Tails
16. Sarnak's Program for Erd\H{o}s Sieves. Part II: Measure Systems and Applications

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/2026-02-27/

1. Simultaneous Approximation for Lattice-Based Cryptography
2. Computing Invariants of Artin-Schreier Curves
3. Analogue of the theta group $\Gamma_{\theta}$
4. Weakening the Legendre Conjecture
5. Multiplicative Diophantine Approximation on Planar Lines with Restricted Denominators
6. An Explicit Result for the Sum of Two Almost Primes
7. On rational quadratic cocycles
8. Distribution of sums involving Dirichlet characters over the $k$-free integers
9. Invertible Calabi-Yau Orbifolds over Finite Fields II
10. Endoscopic transfer and the wavefront upper bound conjecture
11. R-triviality for adjoint classical groups of type C
12. Approximating parametric suprema for constructible and power-constructible functions
13. Toric schemes and integral models for Shimura varieties with $\Gamma_1(p)$-type level

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/2026-02-26/

1. A statistical model for points expanding in higher dimensions while being tied to bijective involutions
2. Prime-Weighted Interference Patterns Inspired by the Euler Product
3. Ours go to 211: Euler pseudoprimes to 47 prime bases (from Carmichael numbers)
4. Quartic del Pezzo surfaces over $\mathbb{F}_p(t)$ without quadratic points
5. Equidistribution for Tannakian monodromy groups
6. The cyclosyntomic regulator of a number field
7. Goldfeld conjecture for non-hyperelliptic direction
8. Second moment of $\textrm{GL(3)} \times \textrm{GL(2)}$ $L$--functions
9. Similitudes over fields with I^4=0
10. Estimates for Character Sums in Finite Fields, $\mathbb{F}_{p^n}$
11. Perfectoid unitary Shimura varieties and $p$-adic Eichler-Shimura map I
12. Side lengths of cubes with vertices in $\mathbb Z^n$
13. An application of Fontaine's monoidal maps to perfectoid towers

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/2026-02-25/

1. Modularity of a certain "rank-2 attractor" Calabi-Yau threefold
2. Algebraic Characterization of Angle Multisections over Rings
3. On Wagstaff primes in the $k$-Lucas number sequence
4. Single conjugacy classes of isometries in orthogonal groups over local fields
5. Solutions of polynomial equations in several variables modulo a prime power
6. On local characterizations of Hida families of Siegel modular forms
7. A Diophantine inequality with five squares of Piatetski-Shapiro primes
8. On the Asymptotic Behavior of a Multiplicative Arithmetic Function Related to the Divisor Function Over Perfect Squares Integers Generated by Shifting
9. Primes in arithmetic progressions to large moduli and refinements of Harman's sieve
10. Rational points on modular curves: parameterization and geometric explanations
11. Distributions of unramified extensions of global fields
12. Torsion points on $\rm{GL}_2$-type abelian varieties
13. Toward the $p$-adic Hodge parameters in the potentially crystalline representations of $\mathrm{GL}_n$
14. Elementary local representation densities at all primes via lifting recursions
15. Potential Relation Between the Riemann Zeta Function and the Polynomial Function $F$ of the Generalized Erd\H{o}s--Straus Conjecture, Subject to its Analytic Continuation
16. Existential theories of henselian valued fields under a formal smoothness assumption
17. Quantum wreath products and $p$-adic general linear group
18. Shifted multiplicative subgroups are not ratio sets

arXiv math.NTの新着論文27本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-02-24/

1. Solving equations of signature $(p,p,2)$ with coefficients over number fields
2. Gain Bounds for Diagonal Superelliptic Equations under the Strong ABC Conjecture
3. Proofs of Lupu's conjectures for multiple zeta values and multiple $t$-values
4. Moduli of $G$-bundles on rigid gerbes over affine curves
5. Congruences for traces of singular moduli and Hurwitz - Kronecker class numbers
6. Arithmetic BF theory and the Cassels-Tate pairing
7. $L^4$-norms of automorphic forms in the depth aspect
8. A cohomological invariant for algebras of degree 8 and exponent 2 in characteristic 2
9. Arithmetic Aspects of Number Fields Generated by Polynomial Families
10. On the analytic continuation of Dirichlet series with missing digits
11. Stacky Batyrev-Manin conjecture and modular curves
12. A new proof of Carlitz-Wan conjecture on exceptional polynomials
13. Modular abelian surfaces of small conductor with nontrivial Tate--Shafarevich groups
14. Nontrivial torsion in the Tate--Shafarevich group via visibility and twists
15. Arithmetic properties of DSOME function
16. Properties of the Function \(F_{x,t}^{(k)}(n)\) with Applications to the Erd\H{o}s--Straus, Sierpi\'nski Conjectures and Their Generalizations
17. Quantitative results on the $k$-dimensional Duffin-Schaeffer conjecture
18. Large fluctuations of random multiplicative functions
19. Subconvexity Problem on $\operatorname{GL}_3$ over number fields: the twist aspect
20. On the Ramanujan Vector Field modulo $p$
21. The number of non-isomorphic arithmetic expressions that can be constructed using +,-,x and /
22. Power partitions and Khinchin families
23. Corrigendum and addendum to "Fixed-point-free elements of iterated monodromy groups" [Trans. of the American Mathematical Society Vol. 367, No. 3 (2015), 2023-2049]
24. Structure of sets with small product sets in torsion-free groups, cyclic groups of prime orders and abelian groups
25. Extreme $L_p$ discrepancy, numerical integration and the curse of dimensionality
26. Monodromy rank and the semisimple Mumford-Tate conjecture for hyper-K\"ahler varieties
27. Hilbert surfaces, modular forms, and Siegel-Veech constants

arXiv math.NTの新着論文7本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-02-23/

1. The Golden Sieve and its connections to Hiccup sequences and Fraenkel games
2. Fermat's Last Theorem for Selmer sections
3. Product of powers of distinct primes as sums of Fibonacci numbers
4. A function field analogue of Ligozat's theorem for Drinfeld modular units
5. Modules of Jacobi forms of degree two of small levels
6. A new class of Correlations insisting on Ramanujan expansions
7. Dynamical GCD Problems and a Variant of the Dynamical Mordell-Lang Conjecture

arXiv math.NTの新着論文6本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-02-20/

1. Algebraic representatives of the ratios $\zeta(2n+1)/\pi^{2n}$ and $\beta(2n)/\pi^{2n-1}$
2. Complex Moments, Gamma and Riemann Zeta Functions unified by the Parabolic Mellin Transform
3. Non-hyperelliptic modular curves of genus 3
4. On the local-global principle for twists of abelian varieties
5. Computing class groups and gonalities of algebraic curves over finite fields
6. Classifying binary quadratic forms using Clifford invariants

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/2026-02-19/

1. On the Lagarias Inequality and Superabundant Numbers
2. On the Jacobian of $\overline{{{\rm Spec}\,\mathbb Z}}$
3. On the Mean Value of a Weighted Composite Arithmetic Function
4. Binomial sums and properties of the Bernoulli transform
5. Quantum modularity of signatures in TQFT and generalized Dedekind sums
6. Intersections of special cycles on Shimura curves and Siegel Maass forms
7. A zero-one law for improvements to Dirichlet's theorem in arbitrary dimension
8. On coefficients, potentially abelian quotients, and residual irreducibility of compatible systems
9. Remarks on the inverse Littlewood conjecture
10. Hensel minimality, $p$-adic exponentiation and Tate uniformization
11. Anticoncentration of Random Sums in $\mathbb{Z}_p$

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/2026-02-18/

1. $\mathcal L$-invariants and deep congruences between newforms
2. Szemer\'edi's Theorem Along Cantor Sets of Integers
3. Relations for partitions with distinct even parts except the largest part which is even
4. On the discriminant and index of a certain class of polynomials
5. A Weighted Words Study of MacMahon's and Russell's Modulo 6 Identities
6. Space-filling lattice designs for computer experiments
7. Subgroups with all finite lifts isomorphic are conjugate
8. Steenrod operations and symplectic arithmetic duality
9. Asymptotics and zero distribution of geometric polynomials
10. Conjugacy classes of regular integer matrices
11. Power monoids and their arithmetic: a survey
12. On Graham's rearrangement conjecture