On the uniform convergence of Poincaré series of exponential type on Jacobi groups
type: Item
instance of: scholarly article
title: On the uniform convergence of Poincaré series of exponential type on Jacobi groups
zbMATH Open document ID: 0867.11036
DOI: 10.1007/BF02940798
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1997-08-10T00:00:00Z
review text: The author studies Jacobi forms on \({\mathcal H}_g\times\mathbb{C}^g\), where \({\mathcal H}_g\) is the Siegel half-space of genus \(g\). He derives absolute uniform convergence of Poincaré series of exponential type in vertical strips (where additionally the boundedness of the real parts in his theorem is required). The basic idea is to verify the Jacobi-Poincaré series essentially as a subseries of the Siegel-Poincaré series of exponential type on \({\mathcal H}_{g+1}\) and to use the known convergence behavior of this type.
Mathematics Subject Classification ID: 11F55
Mathematics Subject Classification ID: 11F46
zbMATH DE Number: 977860
zbMATH Keywords: Siegel modular forms
zbMATH Keywords: Jacobi forms
zbMATH Keywords: uniform convergence
zbMATH Keywords: Poincaré series of exponential type
author: Winfried Kohnen
reviewed by: Aloys Krieg
MaRDI profile type: Publication
cites work: Über die Fourier-Jacobi-Entwicklung Siegelscher Eisensteinreihen
cites work: Q5521721
cites work: On Poincaré series of exponential type on Sp\(_ 2\)
cites work: Non-holomorphic Poincaré-type series on Jacobi groups
cites work: Q5344315
cites work: Q3748348
cites work: Jacobi forms of higher degree
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description: scientific article; zbMATH DE number 977860