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

arXiv math.NTの新着論文5本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-16/

1. Representation of Ramanujan's tau function by twisted divisor functions
2. A proof of $p$-adic Gross--Zagier theorem via BDP formula
3. Fourier Dimension in Duffin--Schaeffer Conjecture
4. Distribution modulo one of linear recurrent sequences
5. $p$-adic Linear Regression for Random Sampling with Digitwise Noise

arXiv math.NTの新着論文8本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-15/

1. Simultaneous non-vanishing of Dirichlet L-functions
2. On the $K$-extensions between Serre weights for unramified $\mathrm{GL}_3$
3. The $p$-adic monodromy theorem over algebraic-affinoid algebras
4. Multivariable automatic arrays and transcendence
5. Solubility for families of norm equations coming from abelian number fields
6. Applications of patching the coherent cohomology of modular curves
7. An inverse theorem for sumsets of sets of positive density in the integers
8. On the number of missing integers in partitions

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/2026-04-14/

1. Order-3 pi-formulas, Apery-like kernels, and Clausen functoriality for Conservative Matrix Fields
2. A comment on the equation $n!!=a_1!!\cdots a_t!!$
3. A formal proof of the Ramanujan--Nagell theorem in Lean 4
4. Low moments of random multiplicative functions twisted by Fourier coefficients of modular forms
5. The Number of Solutions to $ax+by+cz=n$ for Fibonacci and Lucas triplets
6. A note on small theta lift
7. Remarks on Brauer-Manin obstruction for Weil restrictions
8. On the Chevalley-Bass number of a field
9. Conjectural decomposition of symmetric powers of automorphic representations for $\mathrm{GL}(n)$
10. Beatty solutions of almost Golomb equations
11. Regular ternary sums of generalized polygonal numbers
12. Local square mean in the hyperbolic circle problem and sums of Sali\'e sums
13. A Fixed-Prime Criterion for Reciprocals in Missing-Digit Sets
14. Branched covers of $\mathbb{P}^1$ and divisibility in class group
15. The solvability of the inverse volcano problem over non-prime finite fields
16. Almost Free Non-Archimedean Banach Spaces and Relation to Large Cardinals
17. Character values and conductors of low-rank groups of Lie type
18. Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24
19. Geometrization of the Schr\"odinger Model for the Minimal Representation of an Even Orthogonal Group: The de Rham Setting
20. Algorithms on the Pyasetskii involution on local Langlands parameters of classical groups
21. Pro-$p$ Iwahori-Hecke modules in semisimple rank one and singularity categories
22. An analogue of irreducible cuspidal representations for the group $PGL(2)$ over a two-dimensional local field

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/2026-04-13/

1. Galois theory for finite fields
2. Seven squares from three numbers
3. Dedekind zeta functions of non-Galois torsion fields of elliptic curves
4. A Dynamical Lifting Problem For Additive Polynomials
5. Values of algebraic functions at Liouville numbers
6. Identities and transformations for Lambert series and double Lambert series
7. Linear recurrence sequences and palindromic concatenations of two repdigits in base $\beta$
8. Differential operators on locally analytic Shimura varieties
9. Quartic reductions and elliptic obstructions for perfect Euler bricks
10. Bounding the exponential sum on squares of some sifted sequences
11. Modular curves and bad reduction
12. Effective equidistribution of unipotent orbits in homogeneous spaces of $\SL(2,\R)\ltimes(\R^2)^{k}$
13. A Neukirch-Uchida Theorem for 3-Manifolds

arXiv math.NTの新着論文8本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-10/

1. On Lower Bounds for sums of Fourier Coefficients of Twist-Inequivalent Newforms
2. Universal sums of generalized polygonal numbers of almost prime length
3. Proofs for Andrews' Conjectures 5 and 6 on $v_1(q)$
4. A Liouville-Type Inequality for Values of Mahler M-Functions
5. Resurgence of high-energy string amplitudes
6. Lifting banal representations of classical groups
7. L-modules are mixed
8. On a descent conjecture of Wittenberg

arXiv math.NTの新着論文20本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-09/

1. On a perturbed Hofstadter $Q$-recursion
2. Order drop, Hecke descent, and a mod $p^4$ supercongruence for symmetric-cube hypergeometric coefficients
3. The Domb Ap'ery-limit and a proof of the Ramanujan Machine conjecture Z2
4. On the Double Lambert Series Conjecture of Andrews-Dixit--Schultz-Yee
5. The Thue-Morse Transform
6. On canonicity for integral models of Shimura varieties with hyperspecial level
7. Reduced Unitary Whitehead Groups over Function Fields of p-adic Curves
8. Boundary Cohomology of Sp6(Z): Trivial Representation
9. A Hal\'{a}sz-type asymptotic formula for logarithmic means and its consequences
10. Arithmetic intersections on non-split Cartan modular curves
11. Random conic bundle surfaces satisfy the Hasse principle
12. Explicit inequalities for the nth lucky number
13. Weighted averages of arithmetic functions and applications to equidistribution
14. On the cohomology of negative Tate twists via cyclotomic descent
15. On a conjecture of Deines
16. $p$-adic Theory for Partial Toric Exponential Sums
17. Congruence modules and Wiles defects of determinantal rings of maximal minors
18. Short proofs in combinatorics, probability and number theory II
19. Topological Indices of Divisor Prime Graphs
20. A note on complex Lie Algebras isomorphic to their conjugate