A decomposition theorem for Jacobi forms
type: Item
instance of: scholarly article
title: A decomposition theorem for Jacobi forms
zbMATH Open document ID: 0882.11027
DOI: 10.1007/BF01461001
author: Joachim Dulinski
published in: Mathematische Annalen
publication date: 1996-02-01T00:00:00Z
full work available at URL: https://eudml.org/doc/165378
review text: The author proves that the space of Jacobi forms of fixed degree, weight and index decomposes into a direct sum of the subspace of Jacobi cusp forms and subspaces consisting of Klingen-Eisenstein series derived from forms of smaller degree (Theorem 2). Such a decomposition theorem for Siegel modular forms is known due to \textit{H. Klingen} [Math. Z. 102, 30-43 (1967; Zbl 0155.40401)]. A characterization of Eisenstein series of different types by metrical properties using the Petersson scalar product for Jacobi forms is proved (Prop. 7). An application to the Fourier-Jacobi coefficients is given: one shows that in general there are more Jacobi forms than Fourier-Jacobi coefficients of Siegel modular forms (see Appendix).
reviewed by: Andrzej Dąbrowski
Mathematics Subject Classification ID: 11F50
zbMATH DE Number: 840196
zbMATH Keywords: Jacobi forms
zbMATH Keywords: Klingen-Eisenstein series
zbMATH Keywords: Siegel modular forms
MaRDI profile type: Publication
cites work: The theory of Jacobi forms
cites work: Zum Darstellungssatz für Siegelsche Modulformen
cites work: Über Kernfunktionen für Jacobiformen und Siegelsche Modulformen. (Kernel functions for Jacobi forms and Siegel modular forms)
cites work: Q3748348
cites work: Jacobi forms of higher degree
description: scientific article; zbMATH DE number 840196