L-functions of certain exponential sums over finite fields II

TL;DR

This paper computes the $q$-adic slopes of L-functions associated with a specific class of exponential sums over finite fields, utilizing advanced tools from analytic number theory.

Contribution

It extends the understanding of L-functions of exponential sums by explicitly calculating their $q$-adic slopes using toric sum techniques and decomposition theorems.

Findings

Explicit computation of $q$-adic slopes for the class of exponential sums.

Application of Adolphson-Sperber's and Wan's methods to new classes of sums.

Enhanced understanding of the arithmetic properties of these L-functions.

Abstract

In this paper, we compute the $q$-adic slopes of the L-functions of an important class of exponential sums arising from analytic number theory. Our main tools include Adolphson-Sperber's work on toric exponential sums and Wan's decomposition theorems.