The Spectrum of Hyperbolic Surfaces

• Main Author: Bergeron, Nicolas (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Edition: 1st ed. 2016.
• Series: Universitext,
• Subjects: Mathematics.; Harmonic analysis.; Dynamics.; Ergodic theory.; Hyperbolic geometry.; Hyperbolic Geometry.; Abstract Harmonic Analysis.; Dynamical Systems and Ergodic Theory.

This text is an introduction to the spectral theory of the Laplacian on compact or finite area hyperbolic surfaces. For some of these surfaces, called “arithmetic hyperbolic surfaces”, the eigenfunctions are of arithmetic nature, and one may use analytic tools as well as powerful methods in number t...

Table of Contents:

• Preface
• Introduction
• Arithmetic Hyperbolic Surfaces
• Spectral Decomposition
• Maass Forms
• The Trace Formula
• Multiplicity of lambda1 and the Selberg Conjecture
• L-Functions and the Selberg Conjecture
• Jacquet-Langlands Correspondence
• Arithmetic Quantum Unique Ergodicity
• Appendices
• References
• Index of notation
• Index
• Index of names.