The Spectrum of Hyperbolic Surfaces

Nicolas Bergeron

$183.95 $147.13

Paperback

Not in-store but you can order this
How long will it take?

Availability Information

We source books from suppliers in Australia and overseas. For books we don't currently have in stock, the time it takes to get them from our suppliers can vary widely - from a few days to a few months - so we check each book with each supplier to determine the expected time it will take to be supplied to us.

We then advise you accordingly. If the time taken to get any book is too long for you, you can let us know and we will cancel or adjust your order, and refund as required.

To find out the anticipated arrival time for specific items prior to ordering, please contact us by phone or email:

Phone +61 2 9264 3111, or 1800 4 BOOKS (1800 4 26657) if outside Sydney:
option 1 Abbey's Bookshop (Crime, History, Science, Kids & more) • info@abbeys.com.au
option 2 Language Book Centre (ESL & Foreign Languages) • language@abbeys.com.au
option 3 Galaxy Bookshop (Sci-fi, Fantasy, Romance, Graphic Novels) • sf@galaxybooks.com.au

QTY:

English

Springer International Publishing AG
02 March 2016

Complex analysis, complex variables; Non-Euclidean geometry; Non-linear science

Series: Universitext

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.

By: Nicolas Bergeron
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 1st ed. 2016
Dimensions: Height: 235mm, Width: 155mm, Spine: 20mm
Weight: 659g
ISBN: 9783319276649
ISBN 10: 3319276646
Series: Universitext
Pages: 370
Publication Date: 02 March 2016
Audience: College/higher education , A / AS level , Further / Higher Education
Format: Paperback
Publisher's Status: Active

Nicolas Bergeron is a Professor at Université Pierre et Marie Curie in Paris. His research interests are in geometry and automorphic forms, in particular the topology and spectral geometry of locally symmetric spaces.

Reviews for The Spectrum of Hyperbolic Surfaces

The French book under review gives an introduction to hyperbolic surfaces with an emphasis on the Selberg conjecture. ... it is intended for advanced graduate students but is also well suited for all those who want to acquaint themselves with harmonic analysis on hyperbolic surfaces and automorphic forms. (Frank Monheim, zbMATH, August, 2017) This book gives a very nice introduction to the spectral theory of the Laplace-Beltrami operator on hyperbolic surfaces of constant negative curvature. ... mainly intended for students with a knowledge of basic differential geometry and functional analysis but also for people doing research in other domains of mathematics or mathematical physics and interested in the present day problems in this very active field of research. ... book gives one of the best introductions to this fascinating field of interdisciplinary research. (Dieter H. Mayer, Mathematical Reviews, August, 2017)