L-functions of Kloosterman sheaves

2023/05/08 by Yichen Qin, Qin, Yichen · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2305.04882

openalex publication_date 2023/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we study a family of motives M_n+1^k associated with the symmetric power of Kloosterman sheaves, as constructed by Fresán, Sabbah, and Yu. They demonstrated that for n=1, the motivic L-functions of M₂^k extend meromorphically to ℂ and satisfy the functional equations conjectured by Broadhurst and Roberts. Our work aims to extend these results to the motivic L-functions of some of the motives M_n+1^k, with n>1, as well as other related 2-dimensional motives. In particular, we prove several conjectures of Evans type, which relate traces of Kloosterman sheaves and Fourier coefficients of modular forms.

Cited by

• Infinite symmetric power L-functions of the hyper-Kloosterman family
• Comparison between formal slopes and p-adic slopes

Related

• Functional Equations of L-Functions for Symmetric Products of the Kloosterman Sheaf
• Congruences of algebraic L-functions of motives
• Special L-values of geometric motives
• Integral Motivic Sheaves And Geometric Representation Theory
• Geometrization of the local Langlands correspondence, motivically