The Petersson scalar product
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.
scientific article; zbMATH DE number 1251978