Kloosterman sums and Hecke polynomials in characteristics 2 and 3

2020/12/01 by Haessig, C. Douglas
#11L05 #11S40 #11T23 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2012.00570

Abstract

In this paper we give a modular interpretation of the k-th symmetric power L-function of the Kloosterman family of exponential sums in characteristics 2 and 3, and in the case of p=2 and k odd give the precise 2-adic Newton polygon. We also give a p-adic modular interpretation of Dwork's unit root L-function of the Kloosterman family, and give the precise 2-adic Newton polygon when k is odd. In a previous paper, we gave an estimate for the q-adic Newton polygon of the symmetric power L-function of the Kloosterman family when p ≥ 5. We discuss how this restriction on primes was not needed, and so the results of that paper hold for all p ≥ 2.

Related

• 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
• Unit roots of the unit root L-functions of Kloosterman family
• Newton polygons for L-functions of generalized Kloosterman sums
• Infinite symmetric power L-functions of the hyper-Kloosterman family