The spectrum of hyperbolic surfaces
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 ℓℓ́arithmetic hyperbolic surfacesℓℓ́, the eigenfunctions are of arithmetic nature, and one may use analytic tools as well as powerful methods in numb...
| Uniform Title: | Spectre des surfaces hyperboliques. English |
|---|---|
| Main Author: | Bergeron, Nicolas, |
| Other Authors: | SpringerLink (Online service) |
| Format: | eBook |
| Language: | English French |
| Published: |
Cham :
Springer,
2016.
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| Physical Description: |
1 online resource (xiii, 370 pages) : illustrations. |
| Series: |
Universitext.
|
| Subjects: |
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.