Estimations on dimensions of spaces of Jacobi forms
type: Item
instance of: scholarly article
title: Estimations on dimensions of spaces of Jacobi forms
zbMATH Open document ID: 0942.11030
DOI: 10.1007/BF02876566
author: Juping Wang
published in: Science in China. Series A
publication date: 2000-04-19T00:00:00Z
review text: Siegel proved a theorem saying that a Siegel modular form \(f\) of genus \(n\) and weight \(k\) vanishes identically whenever the Fourier coefficients \(\alpha_f(T)\) vanish for \(\text{trace} (T)\leq k\kappa_n\). In the paper under review the author derives an analogous result for Jacobi cusp forms in the sense of Ziegler. This leads to estimates for the dimension of the space of Jacobi cusp forms even for congruence subgroups.
Mathematics Subject Classification ID: 11F50
Mathematics Subject Classification ID: 11F55
zbMATH DE Number: 1274864
zbMATH Keywords: dimension estimates
zbMATH Keywords: Fourier coefficients
zbMATH Keywords: Jacobi cusp forms
reviewed by: Aloys Krieg
MaRDI profile type: Publication
cites work: Der Basissatz für hermitesche Modulformen
cites work: Modular forms on half-spaces of quaternions
cites work: Estimates for dimensions of spaces of Siegel modular cusp forms
cites work: Über die Darstellung der Modulformen \(n\)-ten Grades durch Poincarésche Reihen. (On the representation of modular forms of \(n\)th degree by Poincaré series)
cites work: Jacobi forms of higher degree
cites work: Q3995202
full work available at URL: https://doi.org/10.1007/bf02876566
OpenAlex ID: W2093596280
description: scientific article; zbMATH DE number 1274864