The spectral decomposition of a product of automorphic forms

Abstract

The spectral theory of Roelke and Selberg provides a decomposition of the space of square integrable automorphic forms for the group S L ( 2 ) SL(2) in terms of eigenfunctions of the non-Euclidean Laplacian and of the Hecke operators. The main result of the paper uses the Roelke-Selberg theory to give an interpretation of the L L -functions of Rankin type as "multiplicity factors" in the decomposition of the product of a nonholomorphic Eisenstein series and a cusp form.