On dimension formulas for Jacobi forms
type: Item
instance of: scholarly article
title: On dimension formulas for Jacobi forms
zbMATH Open document ID: 1257.11048
author: Haigang Zhou
author: Tianze Wang
author: Hongwen Lu
published in: Mathematische Zeitschrift
publication date: 2010-02-23T00:00:00Z
review text: The authors consider Jacobi forms of integral weight \(k\) and index \(S\) being a positive definite half-integral \(l\times l\) matrix, which are defined on \(\mathcal{H}_n\times \mathbb{C}^{\; l\times n}\), where \(\mathcal{H}_n\) is the Siegel half-space of degree \(n\). These kinds of Jacobi forms were systematically treated by \textit{C. Ziegler} [Abh. Math. Semin. Univ. Hamb. 59, 191--224 (1989; Zbl 0707.11035)]. In this paper the Selberg trace formula is described explicitly. An application yields an explicit formula of the dimension of the space of Jacobi cusp forms in the case \(n=2, k>l+4, l\) even.
reviewed by: Aloys Krieg
Mathematics Subject Classification ID: 11F50
Mathematics Subject Classification ID: 11F46
Mathematics Subject Classification ID: 11F72
zbMATH DE Number: 5674252
zbMATH Keywords: dimension formula
zbMATH Keywords: Jacobi forms
zbMATH Keywords: Selberg trace formula
zbMATH Keywords: theta series
zbMATH Keywords: Siegel modular forms
MaRDI profile type: Publication
full work available at URL: s00209-009-0539-2
OpenAlex ID: W2083073357
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DOI: 10.1007/S00209-009-0539-2
description: scientific article; zbMATH DE number 5674252