L-functions of Certain Exponential Sums over Finite Fields
Number Theory
2021-07-19 v4
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.
Cite
@article{arxiv.2002.02023,
title = {L-functions of Certain Exponential Sums over Finite Fields},
author = {Chao Chen and Xin Lin},
journal= {arXiv preprint arXiv:2002.02023},
year = {2021}
}