Prime power exponential and character sums with explicit evaluations

Abstract

Exponential and character sums occur frequently in number theory. In most applications one is only interested in estimating such sums. Explicit evaluations of such sums are rare. In this thesis we succeed in evaluating three types of sums when p is a prime and m is sufficiently large. The twisted monomial sum, the binomial character sum, and the generalized Jacobi sum. We additionally show that these are all sums which can be expressed in terms of classical Gauss sums.