On the symmetric fourth power \(L\)-function of \(GL_ 2\)
type: Item
instance of: scholarly article
title: On the symmetric fourth power \(L\)-function of \(GL_ 2\)
zbMATH Open document ID: 0847.11027
DOI: 10.1007/BF02762075
author: David Ginzburg
published in: Israel Journal of Mathematics
publication date: 1996-01-22T00:00:00Z
review text: Let \(G= \text{GL}(2)\) and let \(r\) be the symmetric fourth power representation of the \(L\)-group \(\text{GL}(2, \mathbb{C})\) of \(G\). The author intends to prove that, given a cuspidal representation \(\pi\) of \(\text{GL}(2, \mathbb{A})\), the partial \(L\)-function \(L_S(\pi\otimes \chi, r)\) is holomorphic for generic \(\chi\). In this paper, he introduces a Rankin-Selberg type integral for this \(L\)-function, which involves an Eisenstein series on the double cover of a group of type \(G_2\) and a theta function. This integral is a product of local factors, which are computed at almost all places, and a non-vanishing result is proved. The rest will follow in another article (or articles).
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 22E50
zbMATH DE Number: 836160
zbMATH Keywords: symmetric fourth power representation
zbMATH Keywords: cuspidal representation
zbMATH Keywords: \(L\)-function
zbMATH Keywords: Rankin-Selberg type integral
zbMATH Keywords: product of local factors
zbMATH Keywords: non-vanishing
reviewed by: J. G. M. Mars
MaRDI profile type: Publication
cites work: Q4016336
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full work available at URL: https://doi.org/10.1007/bf02762075
OpenAlex ID: W2318596016
description: scientific article; zbMATH DE number 836160