Fourier coefficients of Siegel-Eisenstein series of odd genus
type: Item
instance of: scholarly article
title: Fourier coefficients of Siegel-Eisenstein series of odd genus
zbMATH Open document ID: 1226.11063
author: Winfried Kohnen
author: YoungJu Choie
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-11-04T00:00:00Z
review text: Generalizing a well-known result (in the case of genus 2) of Eichler and Zagier, the second named author proved an explicit formula for the Fourier coefficients of the holomorphic Siegel-Eisenstein series on the full Siegel modular group of even genus [see Math. Ann. 322, No. 4, 787--809 (2002; Zbl 1004.11020)]. In the paper under review it is shown that a suitable modification of the previous arguments leads to an explicit formula in the case of odd genus as well. In the odd case, only modified divisor sums (and no generalized class numbers as in the even case) enter the final result. Together with the results of the previous work quoted above, the results of this paper give new explicit expressions for all the Fourier coefficients of Siegel-Eisenstein series of both even and odd genus.
reviewed by: Jürgen Elstrodt
Mathematics Subject Classification ID: 11F46
Mathematics Subject Classification ID: 11F30
zbMATH DE Number: 5810262
zbMATH Keywords: Fourier coefficient
zbMATH Keywords: Siegel-Eisenstein series
zbMATH Keywords: Siegel modular groups of odd genus
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.09.019
OpenAlex ID: W2060206750
cites work: Über die Fourierkoeffizienten der Siegelschen Eisensteinreihen
cites work: The theory of Jacobi forms
cites work: An Explicit Formula for Siegel Series
cites work: Dirichlet series in the theory of Siegel modular forms
cites work: Lifting modular forms of half-integral weight to Siegel modular forms of even genus
DOI: 10.1016/J.JMAA.2010.09.019
description: scientific article; zbMATH DE number 5810262