Spectral Theory of Automorphic Functions and Its Applications

Table of Contents
Preface
List of Notations
Chapter 1. Introduction
Chapter 2. What Does One Need Automorphic Functions For? Some Remarks for a Pragmatic Reader
Chapter 3. Harmonic Analysis of Periodic Functions. The Hardy-Voronoĭ Formula
Chapter 4. Expansion in Eigenfunctions of the Automorphic Laplacian on the Lobachevsky Plane
Chapter 5. Harmonic Analysis of Automorphic Functions. Estimates for Fourier Coefficients of Parabolic Forms of Weight Zero
Chapter 6. The Selberg Trace Formula for Fuchsian Groups of the First Kind
Chapter 7. The Theory of the Selberg Zeta-Function
Chapter 8. Problems in the Theory of the Discrete Spectrum of Automorphic Laplacians
Chapter 9. The Spectral Moduli Problem
Chapter 10. Automorphic Functions and the Kummer Problem
Chapter 11. The Selberg Trace Formula on the Reductive Lie Groups
Chapter 12. Automorphic Functions, Representations and L-Functions
Chapter 13. Remarks and Comments. Annotations to the Cited Literature
	Chapter 2. 3. 4.
	Chapter 5
	Chapter 6
	Chapter 7
	Chapter 8
	Chapter 9
	Chapter 10
	Chapter 11
	Chapter 12
References
1-22
23-51
52-84
85-116
117-148
149-183
184-186
Appendix 1. Monodromy Groups and Automorphic Functions
	Commentary
	References
Appendix 2. Automorphic Functions for Effective Solutions of Certain Issues of the Riemann-Hilbert Problem
	Introduction
	1. Fuchsian Groups
	2. Differential Equations
	3. The Riemann-Hilbert Problem for Fuchsian Groups of the First Kind
	4. Equations with Three Singular Points
	5. Additional Information on Fuchsian Groups
	6. The Schwarz Differential Equation and an Algebraic Automorphic Equation
	7. General Variable Change in the Schwarz Equation Defined by the Automorphic Equation
	8. The group Γ*(N) and Its Automorphic Functions
	9. Subgroups of Finite Index of Fuchsian Groups
	10. Subgroups of Finite Index of the Triangular Groups
	11. Subgroups of Finite Index of the Modular Group
	12. The Main Theorem on the Automorphic Equation
	13. \'J-Equations\' of Atkin and Swinnerton-Dyer
	14. Examples of Variable Changes with Controlled Monodromy Groups
	References
	1-6
	7-39
	40-45
Author Index
Subject Index