Mean values of $L$-functions over function fields

Jeffrey Lin Thunder

Vol. 274 (2015), No. 1, 237–256

DOI: 10.2140/pjm.2015.274.237

Abstract

For a fixed global function field, positive integer and complex number, we prove estimates for mean values of $L$-functions evaluated at the given complex number, where the averaging is done over quadratic extensions of the given function field with genus equal to the given positive integer. To accomplish this we utilize our previous results on certain quadratic character sums over function fields.

Keywords

function field, $L$-functions

Mathematical Subject Classification 2010

Primary: 11M41

Milestones

Received: 10 December 2013

Revised: 10 July 2014

Accepted: 10 July 2014

Published: 2 March 2015