Selberg zeta functions associated with a theta multiplier system of \(\mathrm{SL}_2(\mathbb Z)\) and Jacobi forms
type: Item
instance of: scholarly article
title: Selberg zeta functions associated with a theta multiplier system of \(\mathrm{SL}_2(\mathbb Z)\) and Jacobi forms
zbMATH Open document ID: 0737.11016
DOI: 10.1007/BF01444713
author: T. Arakawa
published in: Mathematische Annalen
publication date: 1992-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164955
review text: Certain Selberg zeta functions associated with a theta multiplier system of \(\mathrm{SL}_2(\mathbb Z)\) are defined. The Selberg zeta functions are analytically continued to meromorphic functions in the whole complex plane satisfying certain functional equations by virtue of the general theory of Selberg trace formulas and Selberg zeta functions. The Selberg trace formula discussed in this paper is closely related to the spaces of Jacobi forms. Denote by \(J_{k,m}\) (resp. \(J^*_{k,m})\) the space of holomorphic Jacobi forms (resp. skew-holomorphic Jacobi forms) of weight \(k\) and index \(m\) with respect to \(\Gamma=\mathrm{SL}_2(\mathbb Z)\). Certain relations between the dimensions of the spaces of \(J_{k,m}\), \(J^*_{k,m}\) \((k=1,2)\) and the orders of the zeros at \(s=3/4\) of the Selberg zeta functions are obtained.
Mathematics Subject Classification ID: 11M36
Mathematics Subject Classification ID: 11F50
zbMATH DE Number: 4216037
zbMATH Keywords: Selberg zeta functions
zbMATH Keywords: theta multiplier system
zbMATH Keywords: Selberg trace formula
zbMATH Keywords: Jacobi forms
zbMATH Keywords: dimensions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4216037