The functional equation of the twisted spinor zeta-function and Böcherer's conjecture
type: Item
instance of: scholarly article
zbMATH Open document ID: 0986.11031
author: Michael Kuß
publication date: 2001-07-16T00:00:00Z
full work available at URL: http://www.ub.uni-heidelberg.de/archiv/1436
Mathematics Subject Classification ID: 11F46
Mathematics Subject Classification ID: 11F66
zbMATH DE Number: 1620619
zbMATH Keywords: spinor zeta function
zbMATH Keywords: Siegel modular form
zbMATH Keywords: twists
zbMATH Keywords: Böcherer conjecture
zbMATH Keywords: central critical value
MaRDI profile type: Publication
title: The functional equation of the twisted spinor zeta-function and Böcherer's conjecture
review text: \textit{A. N. Andrianov} [Russ. Math. Surv. 29, No. 3, 45--116 (1974); translation from Usp. Mat. Nauk 29, 43--110 (1974; Zbl 0304.10020)] showed that the spinor zeta function \(Z_F(s)\) of a Siegel modular form \(F\) of genus 2 and weight \(k\) possesses a meromorphic continuation and satisfies a functional equation under \(s\mapsto 2k-2-s\). Later, \textit{W. Kohnen}, \textit{A. Krieg} and \textit{A. Sengupta} [Manuscr. Math. 87, 489--499 (1995; Zbl 0879.11021)] generalized this to twists \(Z_F(s,\chi)\), whenever \(\chi\) is a Dirichlet character such that \(\chi^2\) is primitive and the first Fourier-Jacobi coefficient \(f_1\neq 0\). In his thesis the author drives the analogous result under the weaker assumption that \(\chi\) is primitive. NEWLINENEWLINENEWLINEMoreover, the author investigates the Böcherer conjecture saying that the central critical value \(Z_F(k-1,\chi_D)\), \(\chi_D= (\frac{D}{\cdot})\), is basically a square. This conjecture is numerically verified in several cases.
reviewed by: Aloys Krieg
description: scientific article; zbMATH DE number 1620619