The Petersson scalar product
type: Item
instance of: scholarly article
title: The Petersson scalar product
zbMATH Open document ID: 0934.11018
author: Jürgen Elstrodt
author: Fritz Grunewald
published in: Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)
publication date: 1999-02-21T00:00:00Z
review text: The following topics are covered in this survey article: Petersson's early work on automorphic forms. The Petersson scalar product and its applications to Poincaré series. Simultaneous diagonalization of Hecke operators. Hecke operators on \(\Gamma_0(N)\). Applications to the theory of real analytic automorphic forms. The Petersson scalar product in the theory of modular forms of several variables. The concepts and results are carefully stated and explained, and precise references are given. The bibliography comprises 165 items. The article will be most valuable because it gives quick information on the results and their historical development, and because of its comments on the literature. It will be helpful as a guide for further reading.
reviewed by: Günter Köhler
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 11-02
Mathematics Subject Classification ID: 11F25
Mathematics Subject Classification ID: 11F60
Mathematics Subject Classification ID: 11F46
zbMATH DE Number: 1251978
zbMATH Keywords: survey
zbMATH Keywords: Petersson scalar product
zbMATH Keywords: Poincaré series
zbMATH Keywords: diagonalization of Hecke operators
zbMATH Keywords: real analytic automorphic forms
zbMATH Keywords: modular forms of several variables
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1251978