Fourth power mean of the general $s$-dimensional Kloosterman sum mod $p$

Abstract

In this article, we prove an asymptotic formula for the fourth power mean of a general $s$-dimensional hyper-Kloosterman sum. We find the number of solutions of certain congruence equations mod $p$ which play an integral part to prove our main result. We use estimates for character sums and analytic methods to prove our theorem.