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The spectrum of hyperbolic surfaces

Bergeron, Nicolas.

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The spectrum of hyperbolic surfaces

Record Type:	Electronic resources : Monograph/item
Title/Author:	The spectrum of hyperbolic surfaces/ by Nicolas Bergeron.
Author:	Bergeron, Nicolas.
Published:	Cham :Springer International Publishing : : 2016.,
Description:	xiii, 370 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Spectral theory (Mathematics) -
Online resource:	http://dx.doi.org/10.1007/978-3-319-27666-3
ISBN:	9783319276663$q(electronic bk.)

The spectrum of hyperbolic surfaces
Bergeron, Nicolas.

The spectrum of hyperbolic surfaces[electronic resource] /by Nicolas Bergeron. - Cham :Springer International Publishing :2016. - xiii, 370 p. :ill., digital ;24 cm. - Universitext,0172-5939. - Universitext..

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.

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.

ISBN: 9783319276663$q(electronic bk.)

Standard No.: 10.1007/978-3-319-27666-3doiSubjects--Topical Terms:

524915
Spectral theory (Mathematics)

LC Class. No.: QA685

Dewey Class. No.: 516.9

The spectrum of hyperbolic surfaces
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100 1 $a Bergeron, Nicolas. $3 2183106
240 1 0 $a Spectre des surfaces hyperboliques. $l English
245 1 4 $a The spectrum of hyperbolic surfaces $h [electronic resource] / $c by Nicolas Bergeron.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a xiii, 370 p. : $b ill., digital ; $c 24 cm.
490 1 $a Universitext, $x 0172-5939
505 0 $a 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.
520 $a 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.
650 0 $a Spectral theory (Mathematics) $3 524915
650 0 $a Selberg trace formula. $3 709261
650 0 $a Hyperbolic spaces. $3 555726
650 0 $a Geometry, Hyperbolic. $3 532067
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Hyperbolic Geometry. $3 2072804
650 2 4 $a Abstract Harmonic Analysis. $3 891093
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 891276
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Universitext. $3 812115
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-27666-3
950 $a Mathematics and Statistics (Springer-11649)