SPECTRAL THEORY OF AUTOMORPHIC FUNCTIONS, THE SELBERG ZETA-FUNCTION, AND SOME PROBLEMS OF ANALYTIC NUMBER THEORY AND MATHEMATICAL PHYSICS

Abstract

CONTENTS § 0. Introduction Chapter I. Selberg theory on a compact Riemann surface § 1. The Voronoi-Hardy formula § 2. Elementary spectral theory of automorphic functions § 3. The Selberg trace formula § 4. The Selberg zeta-function § 5. Refinement of the spectral theory of automorphic functions § 6. The problem of moduli Chapter 2. Selberg theory on a fundamental domain of a Fuchsian group of the first kind § 7. The Fuchsian group of the first kind and its fundamental domain § 8. Spectral theory of automorphic functions (general case). The continuous spectrum and Eisenstein-Maass series § 9. The Selberg trace formula (general case) § 10. The Selberg zeta-function (general case) § 11. The discrete spectrum § 12. The Selberg zeta-function of the Dirichlet problem. A refinement of Roelcke's problem References