On a new type of L-function for algebraic curves over finite fields

David Goss

Vol. 105 (1983), No. 1, 143–181

DOI: 10.2140/pjm.1983.105.143

Abstract

Recently there has emerged a new theory of curves over a finite field. This theory is exciting in that it establishes previously unknown analogies between cyclotomic fields and function fields over a finite field. An extremely important aspect of this work is a new type of L-series for these function fields. These L-series bear quite remarkable and exciting similarities to classical L-series of number fields. The purpose of this paper is to describe these new L-series in detail.

Mathematical Subject Classification 2000

Primary: 12A70, 12A70

Secondary: 14G15, 12A90

Milestones

Received: 10 October 1980

Published: 1 March 1983