A remark on the normalization of the standard zeta values for Siegel modular forms
type: Item
instance of: scholarly article
title: A remark on the normalization of the standard zeta values for Siegel modular forms
zbMATH Open document ID: 1221.11116
author: Hidenori Katsurada
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 2010-06-21T00:00:00Z
full work available at URL: http://hdl.handle.net/2115/69749
review text: This note is on the relationship of special values of the standard L-function and congruence of Siegel modular forms. The main result is an improvement of previous results given in [Math. Z. 259, No. 1, 97--111 (2008; Zbl 1173.11029)]. The crucial ingredient is Lemma \(4.2\), a construction of a value \(I\) from a finite dimensional Hermitian vector space \(V\) with given orthogonal basis and two functionals. The values turns out to be independent on the choice of the basis. Finally this type of normalization is applied on the topic of special values, such that the value only depends on the underlying eigenvalue system of the involved cuspidal Hecke eigenform. This leads to Theorem 4.3 which improves the results from the previous paper from above.
Mathematics Subject Classification ID: 11F46
Mathematics Subject Classification ID: 11F33
Mathematics Subject Classification ID: 11F67
zbMATH DE Number: 5723788
zbMATH Keywords: Standard zeta function
zbMATH Keywords: Siegel modular forms
zbMATH Keywords: special values
zbMATH Keywords: congruences
reviewed by: Bernhard Heim
MaRDI profile type: Publication
OpenAlex ID: W2128041918
cites work: Q3754056
cites work: Über die Fourier-Jacobi-Entwicklung Siegelscher Eisensteinreihen. II
cites work: \(p\)-adic measures attached to Siegel modular forms
cites work: Q4253166
cites work: Congruence of Siegel modular forms and special values of their standard zeta functions
cites work: On integrality of Eisenstein liftings
cites work: On Eisenstein series
DOI: 10.1007/S12188-010-0035-Y
description: scientific article; zbMATH DE number 5723788