Jacobi forms and generalized RC-algebras.
type: Item
instance of: scholarly article
title: Jacobi forms and generalized RC-algebras.
zbMATH Open document ID: 1033.11022
published in: Rocky Mountain Journal of Mathematics
publication date: 2003-12-03T00:00:00Z
full work available at URL: CONT31-4.html
review text: Ten years ago \textit{D. Zagier} [Proc. Indian Acad. Sci., Math. Sci. 104, 57--75 (1994; Zbl 0806.11022)] introduced the so-called Rankin-Cohen algebras which consist of differential bilinear operators acting on the graded ring \(M(\Gamma)\) of modular forms with respect to some subgroup \(\Gamma\) of \(\text{PSL}_2 (\mathbb{Z})\). In the paper under review the authors continue their earlier work on Rankin-Cohen brackets with respect to Jacobi forms in the sense of Eichler-Zagier, where the heat operator is involved. In particular they study the algebraic properties of these generalized Rankin-Cohen algebras and give examples generalizing the elliptic case.
Mathematics Subject Classification ID: 11F50
Mathematics Subject Classification ID: 11F60
zbMATH DE Number: 2012012
zbMATH Keywords: Rankin-Cohen algebras
zbMATH Keywords: differential operators
zbMATH Keywords: Jacobi forms
zbMATH Keywords: heat operator
author: YoungJu Choie
author: W. Eholzer
reviewed by: Aloys Krieg
MaRDI profile type: Publication
OpenAlex ID: W1979043142
cites work: Jacobi forms and the heat operator
cites work: Jacobi forms and the heat operator. II
cites work: Rankin-Cohen operators for Jacobi and Siegel forms
cites work: Sums involving the values at negative integers of \(L\)-functions of quadratic characters
cites work: The theory of Jacobi forms
cites work: Algebras of symbols and modular forms
cites work: Modular forms and differential operators
DOI: 10.1216/RMJM/1021249440
description: scientific article; zbMATH DE number 2012012