L-functions of certain exponential sums over finite fields

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.