L-functions of Certain Exponential Sums over Finite Fields

2020/02/05 by Chen, Chao, Lin, Xin
#11L07 #11S40 #11T23 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2002.02023

Abstract

In this paper, we completely determine the slopes and weights 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. One consequence of our main result is a sharp estimate of these exponential sums. Another consequence is to obtain an explicit counterexample of Adolphson-Sperber's conjecture on weights of toric exponential sums.

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