L-Functions for Symmetric Products of Kloosterman Sums

2004/09/20 by Lei Fu, Daqing Wan, Fu, Lei +1
Mathematics · #11L05 #14F20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11L05 #msc:14F20

paper · pdf · doi:10.48550/arxiv.math/0409372

25 pages

openalex publication_date 2004/09/20 · arxiv created 2004/12/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The classical Kloosterman sums give rise to a Galois representation of the function field unramfied outside 0 and ∞. We study the local monodromy of this representation at ∞ using l-adic method based on the work of Deligne and Katz. As an application, we determine the degrees and the bad factors of the L-functions of the symmetric products of the above representation. Our results generalize some results of Robba obtained through p-adic method.

Citations

• Good Reduction of Abelian Varieties

Related

• L-functions of symmetric powers of Kloosterman sums (unit root\n L-functions and p-adic estimates)
• Functional Equations of L-Functions for Symmetric Products of the Kloosterman Sheaf
• Trivial factors for L-functions of symmetric products of Kloosterman sheaves
• L-functions of Symmetric Products of the Kloosterman Sheaf over Z
• Symmetric Power L-functions of the hyper-Kloosterman Family