Spectral Methods of Automorphic Forms

Abstract

Introduction Harmonic analysis on the Euclidean plane Harmonic analysis on the hyperbolic plane Fuchsian groups Automorphic forms The spectral theorem. Discrete part The automorphic Green function Analytic continuation of the Eisenstein series The spectral theorem. Continuous part Estimates for the Fourier coefficients of Maass forms Spectral theory of Kloosterman sums The trace formula The distribution of eigenvalues Hyperbolic lattice-point problems Spectral bounds for cusp forms Classical analysis Special functions References Subject index Notation index.