Square root formulas for central values of Hecke \(L\)-series. II
type: Item
instance of: scholarly article
title: Square root formulas for central values of Hecke \(L\)-series. II
zbMATH Open document ID: 0820.11036
DOI: 10.1215/S0012-7094-93-07215-8
author: Fernando Rodriguez-Villegas
published in: Duke Mathematical Journal
publication date: 1995-09-14T00:00:00Z
review text: The results proved in Part I [the author and \textit{D. Zagier}, Proc. 3rd Conf. Can. Number Theory Assoc., Kingston, Canada 1991, 81-99 (1993; Zbl 0791.11060)] are extended to imaginary quadratic fields with arbitrary odd discriminant \(-d<-3\). More precisely, let \(L(\psi, s)\) be the \(L\)-series attached to a Hecke character \(\psi\) of \(K\) of ``weight \(2k-1\)'', i.e. the associated modular form has weight \(2k\). Then it is shown that to \(\psi\) one can attach a well-defined genus \(G_ \psi\) of \(K\) such that the central value \(L(\psi, k)\) up to a simple normalizing factor is given as the square of the absolute value of a certain linear combination of values of the \((k- 1)\)-st non-holomorphic derivative of a theta series of weight \(k+ 1/2\) at CM points corresponding to ideals in \(G_ \psi\).
reviewed by: Winfried Kohnen
Mathematics Subject Classification ID: 11F67
Mathematics Subject Classification ID: 11R42
zbMATH DE Number: 558969
zbMATH Keywords: Hecke \(L\)-series
zbMATH Keywords: imaginary quadratic fields
zbMATH Keywords: central value
zbMATH Keywords: non- holomorphic derivative of a theta series
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 558969