Sobolev norms of automorphic functionals and Fourier coefficients of cusp forms

Abstract

We propose a new approach to the study of eigenfunctions of the Laplace-Beltrami operator on a Riemann surface of curvature 1. It is based on Frobenius reciprocity from the theory of automorphic functions. We determine Sobolev class of arising automorphic functionals and discuss some applications.