Newton polygons for L-functions of generalized Kloosterman sums

2021/08/02 by Chunlin Wang, Liping Yang, Wang, Chunlin +1
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2108.00676

openalex publication_date 2021/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the Newton polygons for the L-functions of n-variable generalized Kloosterman sums. Generally, the Newton polygon has a topological lower bound, called the Hodge polygon. In order to determine the Hodge polygon, we explicitly construct a basis of the top dimensional Dwork cohomology. Using Wan's decomposition theorem and diagonal local theory, we obtain when the Newton polygon coincides with the Hodge polygon. In particular, we concretely get the slope sequence for L-function of F(λ,x):=∑_i=1ⁿx_i^a_i+λ∏_i=1ⁿx_i^-1.

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