Correspondence among Eisenstein series \(E_{2,1}(\tau,z),H_{3\over 2}(\tau)\) and \(E_ 2(\tau)\)
type: Item
instance of: scholarly article
title: Correspondence among Eisenstein series \(E_{2,1}(\tau,z),H_{3\over 2}(\tau)\) and \(E_ 2(\tau)\)
zbMATH Open document ID: 0890.11017
DOI: 10.1007/BF02677465
published in: Manuscripta Mathematica
publication date: 1998-07-08T00:00:00Z
full work available at URL: https://eudml.org/doc/156293
review text: The classical monograph by \textit{M. Eichler} and \textit{D. Zagier} [The theory of Jacobi forms, Prog. Math. 55 (1985; Zbl 0554.10018)] describes in great detail the correspondences between the space \(J_{k,1}\) of Jacobi forms of weight \(k\) and index 1, Kohnen's ``+'' space \({\mathcal M}_{k-1/2} (\Gamma_0(4))\) and the space \({\mathcal M}_{2k-2} (\Gamma)\) of elliptic modular forms. The paper under review refers to the case \(k=2\) and to the attached Eisenstein series, which are no longer absolutely convergent. In this case one has to apply the Hecke trick in order to obtain similar results. Moreover the correspondences are studied for non-holomorphic Eisenstein series.
Mathematics Subject Classification ID: 11F55
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 11F37
zbMATH DE Number: 1038305
zbMATH Keywords: Jacobi forms of weight 2
zbMATH Keywords: elliptic modular forms
zbMATH Keywords: Eisenstein series
zbMATH Keywords: Hecke trick
zbMATH Keywords: non-holomorphic Eisenstein series
author: YoungJu Choie
reviewed by: Aloys Krieg
MaRDI profile type: Publication
cites work: Sums involving the values at negative integers of \(L\)-functions of quadratic characters
cites work: The theory of Jacobi forms
cites work: Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus
description: scientific article; zbMATH DE number 1038305