Newton polygons of L-functions for two-variable generalized Kloosterman sums

Author:

Wang Chunlin1,Yang Liping2

Affiliation:

1. School of Mathematical Sciences, Sichuan Normal University, Chengdu 610066, P. R. China

2. College of Mathematics and Physics, Chengdu University of Technology, Chengdu 610059, P. R. China

Abstract

In this paper, we study the Newton polygon of the [Formula: see text]-function of a generalized Kloosterman polynomial with two variables over finite fields. We give the explicit form of the monomial basis of the top dimensional cohomology space of the [Formula: see text]-adic complex associated to the [Formula: see text]-function. One consequence of this result is a concrete method for computing the Hodge polygon. Using decomposition theorems of Wan, we determine when a generalized Kloosterman polynomial is ordinary and when its Newton polytope is generically ordinary.

Funder

National Natural Science Foundation of China

national natural science foundation of china

china scholarship council

Publisher

World Scientific Pub Co Pte Ltd

Subject

Algebra and Number Theory

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