On the Fourier expansions of Jacobi forms
type: Item
instance of: scholarly article
title: On the Fourier expansions of Jacobi forms
zbMATH Open document ID: 1116.11031
DOI: 10.1155/S0161171204401185
author: Howard Skogman
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-25T00:00:00Z
full work available at URL: https://eudml.org/doc/53225
review text: Summary: We use the relationship between Jacobi forms and vector-valued modular forms to study the Fourier expansions of Jacobi forms of indexes \(p\), \(p^2\), and \(pq\) for distinct odd primes \(p\), \(q\). Specifically, we show that for such indexes, a Jacobi form is uniquely determined by one of the associated components of the vector-valued modular form. However, in the case of indexes of the form \(pq\) or \(p^2\), there are restrictions on which of the components will uniquely determine the form. Moreover, for indexes of the form \(p\), this note gives an explicit reconstruction of the entire Jacobi form from a single associated vector-valued modular form component. That is, we show how to start with a single associated vector component and use specific matrices from \(\text{SL}_2(\mathbb Z)\) to find the other components and hence the entire Jacobi form. These results are used to discuss the possible modular forms of half-integral weight associated to the Jacobi form for different subgroups.
Mathematics Subject Classification ID: 11F50
Mathematics Subject Classification ID: 11F30
zbMATH DE Number: 2171618
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2171618