On two-term exponential sums and their mean values

Abstract

The mean value problems of exponential sums play a very important role in the research of analytic number theory, and many famous number theory problems are closely related to them. The main purpose of this paper is using some elementary methods and the number of the solutions of the congruence equations to study the calculating problem of some fourth power means of two-term exponential sums, and give exact calculating formulae and asymptotic formula for them.