The Spectrum of Hyperbolic Surfaces

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Geometry
Cover of the book The Spectrum of Hyperbolic Surfaces by Nicolas Bergeron, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Nicolas Bergeron ISBN: 9783319276663
Publisher: Springer International Publishing Publication: February 19, 2016
Imprint: Springer Language: English
Author: Nicolas Bergeron
ISBN: 9783319276663
Publisher: Springer International Publishing
Publication: February 19, 2016
Imprint: Springer
Language: English

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 theory to study them.

After an introduction to the hyperbolic geometry of surfaces, with a special emphasis on those of arithmetic type, and then an introduction to spectral analytic methods on the Laplace operator on these surfaces, the author develops the analogy between geometry (closed geodesics) and arithmetic (prime numbers) in proving the Selberg trace formula. Along with important number theoretic applications, the author exhibits applications of these tools to the spectral statistics of the Laplacian and the quantum unique ergodicity property. The latter refers to the arithmetic quantum unique ergodicity theorem, recently proved by Elon Lindenstrauss.

The fruit of several graduate level courses at Orsay and Jussieu, The Spectrum of Hyperbolic Surfaces allows the reader to review an array of classical results and then to be led towards very active areas in modern mathematics.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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 theory to study them.

After an introduction to the hyperbolic geometry of surfaces, with a special emphasis on those of arithmetic type, and then an introduction to spectral analytic methods on the Laplace operator on these surfaces, the author develops the analogy between geometry (closed geodesics) and arithmetic (prime numbers) in proving the Selberg trace formula. Along with important number theoretic applications, the author exhibits applications of these tools to the spectral statistics of the Laplacian and the quantum unique ergodicity property. The latter refers to the arithmetic quantum unique ergodicity theorem, recently proved by Elon Lindenstrauss.

The fruit of several graduate level courses at Orsay and Jussieu, The Spectrum of Hyperbolic Surfaces allows the reader to review an array of classical results and then to be led towards very active areas in modern mathematics.

More books from Springer International Publishing

Cover of the book High-Tc Copper Oxide Superconductors and Related Novel Materials by Nicolas Bergeron
Cover of the book Recent Advances in Information Systems and Technologies by Nicolas Bergeron
Cover of the book Ionic Liquid Properties by Nicolas Bergeron
Cover of the book Adversary Detection For Cognitive Radio Networks by Nicolas Bergeron
Cover of the book Advances in Water Resources Engineering by Nicolas Bergeron
Cover of the book Design, User Experience, and Usability: Technological Contexts by Nicolas Bergeron
Cover of the book Introduction to Process Control by Nicolas Bergeron
Cover of the book Flood Risk in the Upper Vistula Basin by Nicolas Bergeron
Cover of the book Archaeologies of Early Modern Spanish Colonialism by Nicolas Bergeron
Cover of the book Wireless Power Transfer and Data Communication for Neural Implants by Nicolas Bergeron
Cover of the book Modeling of Nanotoxicity by Nicolas Bergeron
Cover of the book Statistical Applications for Chemistry, Manufacturing and Controls (CMC) in the Pharmaceutical Industry by Nicolas Bergeron
Cover of the book The Labyrinth of Star Formation by Nicolas Bergeron
Cover of the book Energy Geotechnics by Nicolas Bergeron
Cover of the book Satire and Politics by Nicolas Bergeron
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy