Power moments of Kloosterman sums

Abstract

In this paper we give an essential treatment for power moments of Kloosterman sums over the residue class ring Z/qZ of q elements. When q is a large enough power of a prime, we prove concrete formulas using computations with Igusa zeta functions. As a consequence, we show that there are explicit formulas for power moments of Kloosterman sums whenever q is powerful.