プレプリどんどん: math.NT

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/2026-04-30/

1. Estimating the tail of the singular product in the multivariate Bateman-Horn conjecture
2. Combinatorial sums derived from properties of Legendre polynomials
3. Monsky Matrix and 2-Selmer rank
4. The $p$-powers dividing certain exponential sums
5. Solution to the Erdos problem on distinct residues of factorials
6. Families of Unit Equations and Exponential Diophantine Problems via Integral Points
7. Improved bounds for the Fourier uniformity conjecture
8. Generalized Estermann problem for non-integer powers with almost proportional summands
9. On the automorphisms of the power semigroups of a numerical semigroup
10. Multiplicative convolution and double shuffle relations
11. On Arithmetic Mirror Symmetry for smooth Fano fourfolds

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/2026-04-29/

1. Elementary anabelian varieties are anabelian
2. Ramanujan, the taxicab problem for polynomials, and the abc-conjecture
3. Linear recurrences and rational Lambert series
4. Trilinear Kloosterman fractions I: partially fixed moduli and unbalanced convolutions
5. Reciprocity and the Maslov Phase
6. Congruences via Partitions with Exactly Two Part Sizes
7. Additive index and Carlitz rank
8. The Divisor Function along a Deterministic Orbit and the Emergence of Ladders
9. The threshold for linear independence of multiple zeta values in positive characteristic
10. Cyclotomic Numbers of Order $q-1$ over $\mathbb{F}_{q^r}$
11. Some results on naive transcendence in the ring of integers modulo infinitely large primes
12. Conditional Upper Bounds for Large Deviations and Moments of the Riemann Zeta Function
13. On numerical semigroups with embedding dimension four
14. A structure theorem for sets with doubling $4+\delta$
15. The local Langlands correspondence of essentially unipotent supercuspidal representations for disconnected reductive groups
16. A local-global correspondence for perfectoid purity
17. Mild Pro-$p$ Groups and Ordered Monoids

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/2026-04-28/

1. Lattice point visibility along powers of polynomials
2. On the integrality of modular functions over $\mathbb{Z}[j]$ and Kronecker-type congruences
3. A Proof of Bala's General-$m$ Representation of the Harmonic Numbers
4. Core abaci and Diophantine equations I: fundamental weight
5. Hybrid Conjecture in a Mixed Shimura variety
6. Differences of squares of upper-triangular $2\times 2$ integer matrices
7. On (not) learning the M\"obius function
8. A necessary condition for a congruent number of the form $8k+3$
9. $2$-Selmer groups, $2$-class groups, and congruent numbers
10. The Absolute Anabelian Geometry of Virtual Curves of Arbitrary Genus
11. Picking up the partial sums of the M\"{o}bius function problem with probabilistic number theory
12. Large sieve inequality for sums of Legendre symbols over short intervals
13. Unbounded logarithmic limsup in Erd\H{o}s problem 684
14. On optimization on ravine functions. Minkowski-Cohn moduli surface in Cohn parameterization
15. Non-Vanishing of Cubic Twists of $GL_n(\mathbb{Q})$ $L$-functions
16. On the Gauss circle problem over smooth numbers
17. On D-cap-Modules of Finite Length on Rigid Analytic Spaces
18. Linear Bounds for Differentiable Limits of Weak Pair Correlation Functions
19. On $k$-th power Diophantine triples of the form $\{a^k, b, c\}$
20. Joint Sato-Tate Laws for Transformations of Hecke Eigenvalues: The Vertical Case
21. The asymptotic oscillations of moments related to Dirichlet series with missing digits
22. On the hull of linearized polynomial codes
23. A Milestone in Formalization: The Sphere Packing Problem in Dimension 8
24. A note on The asymptotic uniform distribution of subset sums
25. Eleven, twelve, and thirteen lonely runners
26. Dimension of the motivic Galois group of a 1-motive
27. A Necessary and Sufficient Condition for Uniqueness of Euclidean Division
28. Newman's Tauberian theorem, the Riemann-Lebesgue Lemma, and abstract analytic number theory
29. On classical doubling method gamma factors for certain depth zero representations

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/2026-04-27/

1. A link between error terms when counting smooth and rough numbers
2. The exceptional set for Diophantine inequality with mixed powers of primes
3. Exceptional poles of archimedean Rankin-Selberg L-functions for principal series representations of GL(n,R)
4. On a new modular equation of degree five and Eisenstein series identities of associated levels
5. Higher moments of the symmetric square $L$-function off the critical line
6. Matrices with cyclically monotone rows and Cantor numeration systems
7. Khintchine's theorem for inhomogeneous simultaneous approximation with polynomial decay
8. Asymptotic behaviour of analytic torsion and cohomological torsion for $\mathbb{Q}$-rank $1$ arithmetic groups
9. Non-linear geometry of multiple zeta values
10. Numerical Semigroups with $a_e = 2g+1$
11. A construction method for WZ seeds

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/2026-04-24/

1. On the reciprocity law in $\mathbb{F}_{q}[t]$
2. Extremal Problems for GCDs and LCMs in Higher Dimensions
3. Relations between higher level Hurwitz class numbers
4. Moments and joint nonvanishing of symplectic $L$-functions
5. Consecutive non-square nom-primitive pairs in as finite field
6. The Smallest Invariant Factor of Elliptic Curves, and Coincidences
7. Galois representations over convergent de Rham period ring
8. Residues of a tropical zeta function for convex domains
9. Spherical Cap $L_2$ Discrepancy -- Blessing of Dimensionality and a Balanced Large-Cap Variant
10. Lusztig constants and endoscopy

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/2026-04-23/

1. Explicit density computations for certain sets of primes in Lucas sequences
2. On Uniqueness of Mock Theta Functions
3. Minimal $a$-numbers of Artin--Schreier covers of ordinary curves
4. Root numbers for twisted Fermat quotient curves II
5. On the $I(1)$-invariants: Non-abelian Hecke algebra case
6. On the singularities of differential equations satisfied by $E$-functions
7. On the Hyperbolic Fractional Sum of the Divisor Function
8. Non-vanishing of the $p$-adic constant for mock modular forms associated to a newform with real Fourier coefficients
9. On sums of two squares and a basis of order $2$
10. p-adic elliptic polylogarithms and cubic Chabauty
11. Mellin transforms, transfinite diameter and rational approximations of integrals
12. Fractal transference principle for continued fractions of Laurent series

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/2026-04-22/

1. Optimal Shifting Method in Dirichlet's divisor problem
2. Characterizing monogenic trinomials $\boldsymbol{x^{12}+ax^6+b}$ according to their Galois groups
3. Algebraic numbers and Fourier analysis: Salem's third problem
4. Sums of Hecke eigenvalues along polynomial sequences and base change for $\text{GL}(2)$
5. Classification of Rational Functions of Degree Three over Finite Fields
6. Handling some Diophantine equation via Euclidean algorithm and its application to purely exponential equations
7. Beyond the square-root barrier: cubic forms of Perazzo type
8. Quartic Rational Diophantine Quadruples and the Euler Surface
9. Division algorithms for norm-Euclidean imaginary quadratic fields
10. Representations of binary quadratic forms by quaternary quadratic forms
11. Pseudometrics and preorders on sets of integer sequences induced by arithmetic functions functions
12. Explicit counting of ideals in number fields of arbitrary degree
13. Global Product Intersection Sets in Semigroups
14. Independent Sets and Continued Fractions

arXiv math.NTの新着論文30本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-21/

1. M\"obius disjointness conjecture for Furstenberg's flow on $\mathbb{T}^\omega$ in short intervals
2. Reduction mod $p$ of semi-stable representations of some super-Breuil weights
3. Geometry-of-numbers methods over global fields II: Coregular representations
4. On Regular Higher Power Rational Diophantine Triples
5. Non-liftability of Families of Abelian Varieties with Small $l$-adic Local System
6. The Limiting Distribution of Elliptic Dedekind Sums
7. Supersingular Drinfeld modules, Brandt matrices, and rank-metric codes
8. The sum-product phenomenon for dense subsets of finite fields
9. On the normality of the concatenated Fibonacci constant
10. Markov fractions and Cohn matrices
11. Orderings of Generalized k-Markov Numbers
12. Resolutions of spaces of crystalline representations and modularity
13. Effective Joint Sato-Tate Distribution and Sign Change of Symmetric Power Coefficients
14. A remark on an integral structure of the imperfect coefficient ring of $(\varphi,\Gamma)$-modules
15. Explicit Kodaira-Spencer maps over PEL Shimura varieties
16. Semistable Reduction Theorem for Overconvergent $F$-isocrystals over Laurent Series Fields
17. Duality Between Prime Factors and The Prime Number Theorem For Arithmetic Progressions -- Higher Order Dualities
18. Sophie Germain Primes and the Totient of Fibonacci Numbers
19. Solvable Descent and the Grunwald Problem for Solvable Groups
20. A Rademacher exact type formula for pod$_2(n)$
21. Families of symplectic Galois representations over small parabolic eigenvarieties for Siegel cuspforms of genus $2$
22. A primality test for $Kp^\ell - 1$ numbers
23. Maximal quadrics over finite fields and minimal codewords of projective Reed-Muller codes
24. Implementing p-adic numbers in Macaulay2 using its foreign function interface and FLINT
25. Markov numbers of semigroups
26. Elementary symmetric polynomials and a potentially injective family of maps on partitions
27. Forbidden subgraphs in divisor graphs and an Erd\H{o}s divisibility problem
28. Superspecial generalized Howe curves of genus 4, 5, and 6 with completely decomposable Jacobians
29. Unirational algebraic groups and tame ramification
30. Near-optimal density theorems for large dilates of large point configurations

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/2026-04-20/

1. Non-standard Zeckendorf decompositions; or, Tribonacci within Fibonacci
2. Gaussian Behavior and Geometric Gaps in Decompositions from Recurrences with Zero Coefficients
3. Extremal densities for forbidden configurations in $S$-smooth numbers
4. Belyi map verification using certified path tracking
5. Uniform estimates for Delannoy numbers and dimension-free estimates for discrete maximal functions over cross-polytopes
6. On the surjectivity of $(T)$-adic Galois Representations of Drinfeld $A$-Modules of Rank 2 and 3: Density results
7. On a question of Astorg and Boc Thaler
8. Matsuki duality for loop groups
9. Sums of two symbols in $K_2(F)/2K_2(F)$ in characteristic two
10. Adolf Hurwitz and the Fundamental Theorem of Galois Theorie: The K\"onigsberg Lectures of 1890-1891

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/2026-04-17/

1. The level-8 Apery-limit and a proof of the Ramanujan Machine conjecture Z1
2. Arithmetic functions and learning theory
3. Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory
4. On the Number of Prime Factors of Consecutive Integers
5. Computer vision and converse theorems
6. Another factor of integer polynomials with minimal integrals
7. Gelfand--Kirillov dimension and mod $p$ cohomology for inner forms of $\mathrm{GL}_2$
8. Counting Theorems for Algebraic Relations
9. Log-Concavity and Infinite Log-Concavity of Linear Recurrent Sequences with Linear Coefficients via Companion Matrix Methods
10. Recurrence Time for Finite Quantum Systems
11. Distinguished Simple Supercuspidal Representations of $p$-adic $\text{GL}(n)$
12. On local integrability results for $p$-adic reductive groups
13. Evaluations of some series via the WZ method
14. Rational analytic syntomic cohomology
15. Borel--Bernstein and Hirst-type Theorems for Nearest-Integer Complex Continued Fractions over Euclidean Imaginary Quadratic Fields