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The spectrum of hyperbolic surfaces

Bergeron, Nicolas.

The spectrum of hyperbolic surfaces

Record Type:	Electronic resources : Monograph/item
Title/Author:	The spectrum of hyperbolic surfacesby Nicolas Bergeron.
Author:	Bergeron, Nicolas.
Published:	Cham :Springer International Publishing :2016.
Description:	xiii, 370 p. :ill., digital ;24 cm.
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:

182365
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 741028
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 182365
650 0 $a Selberg trace formula. $3 741029
650 0 $a Hyperbolic spaces. $3 190985
650 0 $a Geometry, Hyperbolic. $3 190984
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Hyperbolic Geometry. $3 684054
650 2 4 $a Abstract Harmonic Analysis. $3 274074
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 273794
710 2 $a SpringerLink (Online service) $3 273601
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950 $a Mathematics and Statistics (Springer-11649)