On singular modular forms for principal congruence subgroups
type: Item
instance of: scholarly article
title: On singular modular forms for principal congruence subgroups
zbMATH Open document ID: 1148.11022
published in: Mathematische Zeitschrift
publication date: 2006-11-09T00:00:00Z
review text: Singular automorphic forms on the symplectic group have the property that they are linear combinations of theta series. This well-known property is due to \textit{R. Howe} [Lect. Notes Math. 880, 211--248 (1981; Zbl 0463.10015)]. It is still an open and delicate task to study the level of the theta series and forms involved. In this paper the author considers vector-valued singular modular forms for principal congruence subgroup of the Siegel modular group \(\text{Sp}(n,\mathbb{Z})\). In this important case the author solves the problem completely [see also \textit{E. Freitag}, Singular modular forms and theta relations, Lecture Notes in Mathematics. 1487. Berlin etc.: Springer-Verlag (1991; Zbl 0744.11024)]. The proof involves techniques related to a certain trace operator. Finally the author indicates several generalizations. He makes remarks towards the Igusa subgroup and the optimal level of the theta series.
Mathematics Subject Classification ID: 11F46
Mathematics Subject Classification ID: 11E45
Mathematics Subject Classification ID: 11E10
Mathematics Subject Classification ID: 11F27
zbMATH DE Number: 5071439
zbMATH Keywords: Siegel modular forms
zbMATH Keywords: theta series
zbMATH Keywords: trace operator
zbMATH Keywords: principal congruence subgroup
author: Francesco Ludovico Chiera
reviewed by: Bernhard Heim
MaRDI profile type: Publication
full work available at URL: s00209-005-0911-9
OpenAlex ID: W2044884761
cites work: Q3754056
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DOI: 10.1007/S00209-005-0911-9
description: scientific article; zbMATH DE number 5071439