, Volume 327, Issue 2, pp 315-338
Date: 13 Aug 2003

Double Dirichlet series and the n -th order twists of Hecke L -series

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


Let n≥3 be a fixed integer and let F be a global field containing the n-th roots of unity. In this paper we study the collective behavior of the n-th order twists of a fixed Hecke L-series for F. To do so, we introduce a double Dirichlet series in two complex variables (s, w) which is a weighted sum of the twists, and obtain its meromorphic continuation. We also study related sums of n-th order Gauss sums. These objects together satisfy a nonabelian group of functional equations in (s, w) of order 32.