On the characterization of skew-holomorphic Jacobi-forms
type: Item
instance of: scholarly article
title: On the characterization of skew-holomorphic Jacobi-forms
zbMATH Open document ID: 0849.11040
DOI: 10.1007/BF02953337
author: Rolf Berndt
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1996-06-19T00:00:00Z
review text: The author and \textit{S. Böcherer} [Math. Z. 204, 13-44 (1990; Zbl 0695.10024)] have given a characterization of the space of holomorphic Jacobi forms of weight \(k\) and index \(m\) in the sense of Eichler-Zagier in terms of the discrete series representation \(\pi^+_{m,k}\) of the Jacobi group. Meanwhile \textit{N. P. Skoruppa} [in Automorphic functions and their applications, Int. Conf., Khabarovsk/USSR 1988, 167-185 (1990; Zbl 0745.11029)] also introduced skew-holomorphic Jacobi forms. The author shows that they can be characterized as functions on the Jacobi group realizing vectors of dominant weight for the discrete series representation \(\pi^-_{m,k}\).
Mathematics Subject Classification ID: 11F50
Mathematics Subject Classification ID: 11F70
zbMATH DE Number: 878388
zbMATH Keywords: skew-holomorphic Jacobi forms
zbMATH Keywords: Jacobi group
zbMATH Keywords: discrete series representation
reviewed by: Aloys Krieg
MaRDI profile type: Publication
cites work: SIEGEL'S FORMULA FOR JACOBI FORMS
cites work: Die Jacobigruppe und die Wärmeleitungsgleichung. (The Jacobi group and the heat equation)
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cites work: Jacobi forms and discrete series representations of the Jacobi group
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cites work: Q3979378
full work available at URL: https://doi.org/10.1007/bf02953337
OpenAlex ID: W1986834907
description: scientific article; zbMATH DE number 878388