Evaluation of Kloosterman and Salié sums for arbitrary number fields

Abstract

Let K be a number field with ring of integers O. Let I be an ideal in O and let φ, ψ be characters of the abelian group O/I. We shall denote by (O/I)b the character group of O/I. We shall consider the following exponential sums: the generalized Kloos- terman sums and the generalized Salie sums. The main purpose of this paper is to give methods for the evaluation of these sums explicitly.