A weak multiplicity-one theorem for Siegel modular forms.
type: Item
instance of: scholarly article
title: A weak multiplicity-one theorem for Siegel modular forms.
zbMATH Open document ID: 1050.11052
author: Rudolf Scharlau
author: Lynne H. Walling
published in: Pacific Journal of Mathematics
publication date: 2004-09-16T00:00:00Z
review text: Let \(F\), \(G\) be two Siegel modular forms of degree \(n\) with respect to some congruence subgroup \(F_{n,0}(l)\) and some character. Suppose that \(F\), \(G\) are eigenforms with respect to the Hecke operator \(T_n(p)\), \(p\) prime, with the same eigenvalues. If their Fourier coefficients agree on all primitive lattices and 0, then \(F=G\). The result generalizes the case \(n=2\) by \textit{S. Breulmann} and \textit{W. Kohnen} [Nagoya Math. J. 155, 153--166 (1999; Zbl 0936.11030)]. The proof is quite different and involves only elementary algebraic arguments.
Mathematics Subject Classification ID: 11F46
Mathematics Subject Classification ID: 11F30
zbMATH DE Number: 2101115
zbMATH Keywords: Siegel modular forms
zbMATH Keywords: Hecke eigenforms
zbMATH Keywords: multiplicity-one theorem
zbMATH Keywords: Fourier coefficients
reviewed by: Aloys Krieg
MaRDI profile type: Publication
full work available at URL: pjm.2003.211.369
OpenAlex ID: W2122799639
DOI: 10.2140/PJM.2003.211.369
description: scientific article; zbMATH DE number 2101115