The Siegel-Jacobi operator
type: Item
instance of: scholarly article
title: The Siegel-Jacobi operator
zbMATH Open document ID: 0790.11040
DOI: 10.1007/BF02941338
author: V. Pereyra
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1994-01-31T00:00:00Z
review text: The author considers Jacobi forms of several variables with respect to the representation \(\varrho\) and the index \(\mathcal M\), which is a half- integral semipositive matrix, in the sense of \textit{C. Ziegler} [Abh. Math. Semin. Univ. Hamb. 59, 191-224 (1989; Zbl 0707.11035)]. A Siegel \(\Phi\)-operator for these spaces of Jacobi forms is introduced. In the particular case, when \(2{\mathcal M}\) is unimodular, sufficient conditions on the weight of \(\varrho\) are derived such that the Siegel \(\Phi\)-operator is injective resp. surjective. Moreover the commutation relations with Hecke operators are described.
Mathematics Subject Classification ID: 11F55
Mathematics Subject Classification ID: 11F46
zbMATH DE Number: 492589
zbMATH Keywords: Jacobi forms of several variables
zbMATH Keywords: Siegel \(\Phi\)-operator
zbMATH Keywords: Hecke operators
reviewed by: Aloys Krieg
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 492589