L-functions of symmetric powers of the generalized Airy family of exponential sums

2010/08/02 by C. Douglas Haessig, Haessig, C. Douglas, Antonio Rojas‐León +2
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1008.0408

12 pages

arxiv created 2010/08/02 · openalex publication_date 2010/08/02 · arxiv updated 2010/08/04 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

This paper looks at the L-function of the k-th symmetric power of the ell-adic sheaf over the affine line associated to the generalized Airy family of exponential sums. We compute the degree of this rational function and the local factors at infinity.

Citations

• Calculation of l-adic local Fourier transformations

Related

• L-functions of symmetric powers of the generalized Airy family of exponential sums: ell-adic and p-adic methods
• L-functions of symmetric powers of Kloosterman sums (unit root\n L-functions and p-adic estimates)
• Symmetric Power L-functions of the hyper-Kloosterman Family
• Trivial factors for L-functions of symmetric products of Kloosterman sheaves
• L-functions of certain exponential sums over finite fields II