Construction of Jacobi cusp forms
type: Item
instance of: scholarly article
title: Construction of Jacobi cusp forms
zbMATH Open document ID: 0921.11025
author: Hiroshi Sakata
published in: Proceedings of the Japan Academy. Series A
publication date: 1999-09-29T00:00:00Z
review text: In [\textit{Y. J. Choie, H. Kim} and \textit{M. I. Knopp}, Math. Z. 219, 71-76 (1995; Zbl 0822.11040)] the authors carried out the construction of a Jacobi cusp form \(f(\tau,z)\) from a pair \(\{h(\tau,z),g(\tau)\}\) consisting of a Jacobi cusp form and an ordinary modular cusp form. There, the coefficients of \(f(\tau,z)\) are defined to be Rankin-Selberg convolution of the Dirichlet series arising as the Mellin transforms of \(h\) and \(g\). This construction is a special case of the general method described by \textit{W. Kohnen} [Math. Z. 207, 659-660 (1991; Zbl 0744.11026)]. In the article under review, the author extends the 1995 result by replacing \(g(\tau)\) with a Jacobi cusp form.
Mathematics Subject Classification ID: 11F55
Mathematics Subject Classification ID: 11F30
zbMATH DE Number: 1268563
zbMATH Keywords: construction of Jacobi cusp forms
zbMATH Keywords: Fourier coefficients
zbMATH Keywords: Rankin-Selberg convolution
MaRDI profile type: Publication
full work available at URL: pjaa.74.117
OpenAlex ID: W2089748294
cites work: Rankin's method and Jacobi forms
cites work: Construction of Jacobi forms
cites work: The theory of Jacobi forms
cites work: Heegner points and derivatives of \(L\)-series. II
DOI: 10.3792/PJAA.74.117
description: scientific article; zbMATH DE number 1268563