\(L\)-functions on \(GSp_2\times Gl_2\) of mixed weights
type: Item
instance of: scholarly article
title: \(L\)-functions on \(GSp_2\times Gl_2\) of mixed weights
zbMATH Open document ID: 0967.11017
author: Siegfried Böcherer
author: Bernhard Heim
published in: Mathematische Zeitschrift
publication date: 2001-08-31T00:00:00Z
review text: Let \(g\) be a holomorphic Siegel cusp form of degree 2 and weight \(k\) and let \(h\) be a holomorphic elliptic cusp form of weight \(l\) (\(k\) and \(l\) even, \(\geq 2\)). Assume \(g\) and \(h\) are Hecke eigenforms and the first Fourier-Jacobi coefficient of \(g\) is not identically zero. The authors prove the meromorphic continuation and functional equation of the \(L\)-function attached to \(g\) and \(h\). In case \(k=l\) this is contained in \textit{B. Heim} [Proc. Symp. Pure Math. 66, 201-238 (1999; Zbl 1001.11019)]. In the present paper differential operators are applied to one of the factors in the integrand of the integral representation of the \(L\)-function to obtain the result for arbitrary weights. The cases \(k\geq l\) and \(k<l\) demand different treatment.
Mathematics Subject Classification ID: 11F66
Mathematics Subject Classification ID: 11F46
Mathematics Subject Classification ID: 11F55
zbMATH DE Number: 1533431
zbMATH Keywords: \(L\)-function
zbMATH Keywords: meromorphic continuation
zbMATH Keywords: functional equation
zbMATH Keywords: Siegel cusp form
zbMATH Keywords: elliptic cusp form
reviewed by: J. G. M. Mars
MaRDI profile type: Publication
full work available at URL: s002090000121
OpenAlex ID: W184250508
DOI: 10.1007/S002090000121
description: scientific article; zbMATH DE number 1533431