On automorphic forms for the Jacobi group
type: Item
instance of: scholarly article
title: On automorphic forms for the Jacobi group
zbMATH Open document ID: 0822.11042
author: Rolf Berndt
published in: Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)
publication date: 1995-07-04T00:00:00Z
review text: The paper under review contains a survey about the theory of Jacobi forms. The author starts with the definition of the Jacobi group \(G^ J\) as the semi-direct product of \(SL_ 2 (\mathbb{R})\) with the Heisenberg group and sketches the historical development of the theory of Jacobi forms. Then the general theory of automorphic forms for reductive groups is compared with the one for the non-reductive group \(G^ J\). Next the connection between Jacobi forms and the discrete series representation of \(G^ J\) is explained. The final part is devoted to the question how to establish a canonical theory of \(L\)-functions for Jacobi forms, for instance by using Whittaker models.
Mathematics Subject Classification ID: 11F55
Mathematics Subject Classification ID: 11F66
Mathematics Subject Classification ID: 11-02
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 32N10
zbMATH DE Number: 770143
zbMATH Keywords: survey
zbMATH Keywords: Jacobi forms
zbMATH Keywords: Jacobi group
zbMATH Keywords: historical development
zbMATH Keywords: discrete series representation
zbMATH Keywords: \(L\)-functions
zbMATH Keywords: Whittaker models
reviewed by: Aloys Krieg
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 770143