Fourier-Jacobi expansion and the Ikeda lift
type: Item
instance of: scholarly article
title: Fourier-Jacobi expansion and the Ikeda lift
zbMATH Open document ID: 1272.11064
author: Shuichi Hayashida
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 2011-11-04T00:00:00Z
review text: In 2001 \textit{T. Ikeda} [Ann. Math. (2) 154, No. 3, 641--681 (2001; Zbl 0998.11023)] constructed a lifting from elliptic modular forms to Siegel modular forms of any degree. The existence of such lifting has previously been conjectured by W. Duke and Ö. Imamoglu and by T. Ibukiyama, independently. Since the Ikeda lift is a generalization of the Saito-Kurokawa lift for arbitrary even degree, it is natural to investigate the Fourier-Jacobi coefficients of Siegel modular forms generated by the Ikeda lift. In this article, the author considers such a Fourier-Jacobi expansion of Siegel modular forms generated by the Ikeda lift having two purposes in mind: first, to give an expression of \(L\)-function of certain Siegel modular forms of half-integral weight of odd degree; and secondly, to give a relation among Fourier-Jacobi coefficients of Siegel modular forms generated by the Ikeda lift.
reviewed by: Olaf Ninnemann
Mathematics Subject Classification ID: 11F46
Mathematics Subject Classification ID: 11F37
Mathematics Subject Classification ID: 11F30
Mathematics Subject Classification ID: 11F50
Mathematics Subject Classification ID: 11F66
zbMATH DE Number: 5968103
zbMATH Keywords: Siegel modular forms
zbMATH Keywords: Jacobi forms
zbMATH Keywords: Maass relation
zbMATH Keywords: Fourier-Jacobi coefficients
MaRDI profile type: Publication
full work available at URL: s12188-011-0053-4
OpenAlex ID: W2036122987
cites work: Q4835075
cites work: On a conjecture of Duke-Imamoglu
cites work: Sums involving the values at negative integers of \(L\)-functions of quadratic characters
cites work: The theory of Jacobi forms
cites work: THE ACTION OF MODULAR OPERATORS ON THE FOURIER-JACOBI COEFFICIENTS OF MODULAR FORMS
cites work: Zeta function and Zharkovskaya's theorem on Siegel modular forms of half-integral weight
cites work: Q4272876
cites work: On the lifting of elliptic cusp forms to Siegel cusp forms of degree \(2n\)
cites work: Lifting modular forms of half-integral weight to Siegel modular forms of even genus
cites work: A Maass space in higher genus
cites work: Nearly holomorphic Eisenstein liftings
cites work: L-functions attached to Jacobi forms of degree n. Part I. The basic identity.
cites work: Q3475326
cites work: On modular forms of half integral weight
cites work: A trace formula for Jacobi forms.
cites work: Q3748348
cites work: Q3474716
cites work: Q3037541
cites work: Q3322181
cites work: Jacobi forms of higher degree
DOI: 10.1007/S12188-011-0053-4
description: scientific article; zbMATH DE number 5968103