On analytic properties of the standard zeta function attached to a vector-valued modular form
type: Item
instance of: scholarly article
title: On analytic properties of the standard zeta function attached to a vector-valued modular form
author: Yanyan Li
published in: Research in Number Theory
publication date: 2022-10-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/2108.06540
review text: The main objective of the present paper is to examine the analytic properties of a certain \(L\)-function of a vector-valued modular form of type \(\rho_{L,1}\) which is a finite dimensional representation of the symplectic modular group \(\mathrm{SL}(2,\mathbb{Z})\). The main tool in this regard is to prove the Garret-Böcherer decomposition of a non-holomorphic vector-valued Siegel Eisenstein series \(E^2_{l,0}\). As consequence, it is shown that the standard zeta function associated to a vector-valued common eigenform \(f\) for the Weil representation \(\rho_{L,1}\) can be meromorphically continued to the whole complex plane and that it satisfies a functional equation.
reviewed by: Sami Omar
Mathematics Subject Classification ID: 11F66
Mathematics Subject Classification ID: 11F27
Mathematics Subject Classification ID: 11F25
Mathematics Subject Classification ID: 11M41
zbMATH DE Number: 7608399
zbMATH Keywords: vector-valued modular forms for the Weil representation
zbMATH Keywords: standard zeta function
zbMATH Keywords: Garret-Böcherer decomposition
MaRDI profile type: Publication
OpenAlex ID: W3193397979
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DOI: 10.1007/S40993-022-00368-Z
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description: scientific article; zbMATH DE number 7608399