On the Dwork trace formula

Alan Adolphson

Vol. 113 (1984), No. 2, 257–268

DOI: 10.2140/pjm.1984.113.257

Abstract

We prove a generalization of Dwork’s trace formula for certain completely continuous operators on p-adic Banach spaces. This generalization makes it simpler to apply Dwork’s theory to the study of certain exponential sums involving both additive and multiplicative characters. As an example, we treat the case of Gauss sums and give a new proof of the Gross-Koblitz formula.

Mathematical Subject Classification 2000

Primary: 11T21, 11T21

Secondary: 11S80

Milestones

Received: 13 September 1982

Published: 1 August 1984