Some problems on exponential sums

Abstract

The central theme of this thesis is to study the moments of certain exponential sums which we primarily capture by some asymptotic formulas Our results are conceptual advancements to previously known methods and results on Kloosterman sums generalized Gauss sums and double exponential sums Firstly we introduce some new techniques to find the number of solutions of certain congruence equations modulo a prime p which eventually allow us to obtain a sharper bound compared to previously k...