Estimates for dimensions of spaces of Siegel modular cusp forms
type: Item
instance of: scholarly article
title: Estimates for dimensions of spaces of Siegel modular cusp forms
zbMATH Open document ID: 0867.11033
DOI: 10.1007/BF02940813
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1997-08-10T00:00:00Z
review text: The authors give upper bounds for the dimension of the space \(S^k_n\) of Siegel cusp forms of degree \(n\) and weight \(k\). In particular, they provide various sets of Fourier-Jacobi coefficients, whose vanishing implies that the associated \(f\in S^k_n\) is identically zero. This approach generalizes Siegel's and Eichler's methods. As an example they are able to show that the Siegel theta series of degree \(n\) attached to the lattices \(E_8\oplus E_8\) and \(D^+_{16}\) coincide if and only if \(n\leq 3\) by computing just one Fourier coefficient.
Mathematics Subject Classification ID: 11F46
Mathematics Subject Classification ID: 11F30
Mathematics Subject Classification ID: 11F27
zbMATH DE Number: 977875
zbMATH Keywords: dimension estimates
zbMATH Keywords: Siegel cusp forms
zbMATH Keywords: Fourier-Jacobi coefficients
zbMATH Keywords: Siegel theta series
author: Cris Poor
author: David S. Yuen
reviewed by: Aloys Krieg
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 977875