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/2026-05-05/

1. Monogenic Fields from Polynomial Compositions with Applications
2. Sets of integers satisfying Bateman-Horn statistics
3. Bowen--Franks groups and minus class groups of cyclotomic number fields with prime conductor
4. A logarithmic structure theorem for multiplicative functions with small partial sums
5. 3-class field towers with 2 or 3 stages
6. A note on bilinear sums with modular square roots
7. Archimedean arithmetic Siegel--Weil formula for general weights over Shimura curves
8. Numbers in a Beatty sequence which are orders only of cyclic, abelian or nilpotent groups
9. On the generalized inverse tangent integral and Catalan's constant
10. Gaps in Multiplicative Sidon Sets
11. On the Sum of a Prime and a Number that is not Square-Free
12. Expansion in $\text{SL}_2(\mathbb Z/q\mathbb Z)$ and Zaremba's conjecture
13. Cusp forms and parabolic cohomology classes for symmetric spaces of rank one
14. The generalized Fermat equation $Ax^2 + By^r = Cz^p$ and applications
15. Reductions of $\mathrm{GL}_2(\mathbb Q_{p^f})$-Banach spaces of slopes in $(0,1)$
16. A bibasic double sum extension of a $q$-binomial theorem arising out of subspace enumeration
17. Flat Cohomological Purity for Syntomic Schemes over Valuation Rings
18. On conjectural fermionic formulas for the Macdonald index in Argyres-Douglas theories
19. Twisting Higgs Modules and Functorial Aspects of the p-adic Simpson Correspondence

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/2026-05-04/

1. The cardinality of a set containing the pairwise sums of a fixed number of integers
2. Primitive sets and von Mangoldt chains: Erd\H{o}s Problem #1196 and beyond
3. Effective multi-equidistribution for translates of unipotent flows and Central limit theorems in inhomogeneous Diophantine approximation
4. Notes on Algebraic Properties and Non-Standard Analysis of the Ring of Integers Modulo Infinitely Large Primes
5. Exponent-one blockers and a Mordell-Weil construction of Euler bricks
6. The Hurwitz sum-of-squares problem depends on the base field
7. Modular Forms and Numerical Explorations of Rational Approximations to $\zeta(3)$
8. On divisor sums due to Erd\H{o}s and Ramanujan
9. Lang-Trotter phenomena and unlikely intersections
10. A note on Zilber-Pink in $Y(1)^n$
11. Conjectural duality for iterated $q$-integrals on $\mathbb{P}^{1}$ minus four generic points
12. On convex bodies with constant non-central sections
13. Delta characters and crystalline cohomology of abelian schemes
14. On the largest sum-free subset of the lattice cube

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/2026-05-01/

1. An $O_K$-basis for the image of a Lubin-Tate logarithm on $\pi$-regular extensions of $K$
2. Mod p Monodromy of Cyclic Covers of the Projective Line
3. Simple Lie Groups of type An as Galois groups over Q
4. On the difference between perfect powers and integral $S$-units
5. An improved non-linear Roth-type theorem in finite fields
6. A divisor function of Wigert and higher degree forms
7. Frobenius Traces for Rank-2 Drinfeld Modules, Higher-Dimensional Galois Representations, and a Strong Multiplicity One Theorem in Positive Characteristic
8. A torsion-intersection proof of perfect-cuboid nonexistence on 1,072 explicit master-tuple fibers
9. Asymptotic Vanishing of Stiefel--Whitney Classes for $\mathrm{GL}_n(\mathbb{F}_q)$
10. Polynomial Maps with Constants on Matrix Algebra
11. The proportion of permutations fixing a $k$-set

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