178 papers
This paper establishes several inequalities comparing formal slopes with p-adic slopes of solvable differential modules over the punctured open unit disc by analyzing Newton polygons and the log-convexity of generic radius functions.
This paper demonstrates that adjoining -adic analogs of and to the ring of analytic functions on the Fargues-Fontaine curve eliminates its Galois cohomology in degrees , thereby enabling the formulation of and -type conjectures for the compact support cohomology of -adic analytic varieties.
This paper establishes explicit formulas for a quantum invariant functor on projective varieties over number fields, with a detailed analysis of the specific case involving abelian varieties with complex multiplication.
This paper investigates the asymptotic counting of matrices over finite fields that commute with their Frobenius image (and its iterates), providing explicit results for specific cases such as size-2, diagonalizable, and -defined eigenspace matrices while outlining the approach for the general case.
This paper establishes an explicit formula for the -polynomials of van der Geer--van der Vlugt curves in characteristic 2 by leveraging the structure of Heisenberg groups and Lang torsors, ultimately enabling the construction of examples that attain the Hasse--Weil bound.
This paper establishes a unified framework for proving the almost everywhere pointwise convergence of sparse ergodic averages in for both deterministic and random sequences within specific parameter ranges, while providing new quantitative convergence estimates that improve upon previous non-quantitative results.
This paper investigates the inverse problem of determining the properties of a quadratic number field based on the growth of an elliptic curve's torsion subgroup defined over the rationals, establishing an explicit relationship between the primes dividing the curve's conductor and the conductor of the field extension.
Motivated by prior work on post-critically finite cubic polynomials, this paper proposes a Markov model based on critical orbits to describe the factorization of iterated PCF cubic polynomials over and constructs groups that are conjectured to contain the Galois groups of these iterations.
This paper computes the height filtration and successive minima of the height function associated with a relatively ample line bundle on a flag bundle over a smooth projective curve defined over an algebraically closed field of positive characteristic.
This paper investigates two-color partitions with odd smallest parts and specific restrictions on even parts, establishing congruences modulo 2 and 4 for their counts, deriving closed-form eta-quotient generating functions, and formulating Ramanujan-type congruences for the limiting sequence as the restriction parameter tends to infinity.
This paper confirms Oort's conjecture by proving that for even and , every geometric generic member of the maximal supersingular Ekedahl-Oort stratum in the moduli space of principally polarized abelian varieties has an automorphism group consisting only of , while also establishing the result for the specific case of for any prime .
This paper introduces a simplified perspective on Hodge-Newton indecomposability to provide a uniform proof of a combinatorial identity derived from affine Deligne-Lusztig varieties with finite Coxeter parts.
This paper establishes results on distinguishing Siegel cusp forms of degree two, demonstrating that a level-one Hecke eigenform can be uniquely determined by its second Hecke eigenvalue under a specific assumption and that two such eigenforms can be distinguished using -functions.
This paper provides a comprehensive catalog of Lambert series identities, detailing their formal properties, combinatorial generalizations, and connections to partition functions, while offering a reference compendium of known formulas for various special cases without focusing on rigorous analytic convergence.
This paper presents and proves the existence of an efficient algorithm for computing -expansions of classical modular forms of arbitrary weight and level for any congruence subgroup, while also providing the necessary theoretical background and practical implementation details.
This paper investigates the distribution of boundary points of expansion to establish a lower bound on the mutual distances between runners on a circular track under specific equidistant spacing conditions, thereby providing a partial application toward the Lonely Runner Conjecture.
This paper introduces and develops the concept of ramification within a given modulus, exploring its properties and its potential connections to significant mathematical problems, particularly the Goldbach conjecture.
This paper presents a fully device-resident, multi-GPU architecture that achieves near-zero host-device communication and 99.7% parallel efficiency through lock-free work-stealing and optimized shared-memory tiling, enabling the verification of Goldbach's conjecture up to $10^{13}$ in just 133.5 seconds on a four-GPU system with a 45.6× speedup over previous methods.
This paper establishes the theorem of the heart for Weibel's homotopy -theory (), proving that the realization functor induces an equivalence for small stable -categories with bounded -structures, a result derived from a strengthened version of Barwick's theorem that provides precise isomorphism ranges for classical -theory and demonstrates the sharpness of these bounds.
This paper investigates congruences between Hecke eigenvalues of Hermitian Klingen-Eisenstein series and cusp forms on the unitary group over , while also establishing the rationality of the space of Hermitian automorphic forms and the integrality of their Hecke eigenvalues.