TWISTS OF HECKE L-FUNCTIONS

The purpose of this note is to give a simple proof of Theorem 3 below, a statement about the nonvanishing of certain Hecke L-functions of CM fields formed from Hecke characters of prescribed infinity type. The need for such a result arose in work of Dinakar Ramakrishnan, whom I thank for bringing the problem to my attention. Let K be a CM field and F its maximal totally real subfield. We shall use the term “ray class character” as a synonym for ”idele class character of finite order”. Note that for a totally complex field such as K, this notion coincides with “idele class character trivial at the infinite places”. © 1992, Walter de Gruyter. All rights reserved.