LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	516.9
Title	The Spectrum of Hyperbolic Surfaces ([EBook]) / by Nicolas Bergeron.
Author	Bergeron, Nicolas
Other name(s)	SpringerLink (Online service)
Edition statement	1st ed. 2016.
Publication	Cham : : Springer International Publishing : : Imprint: Springer, , 2016.
Physical Details	XIII, 370 p. 8 illus. in color. : online resource.
Series	Universitext 0172-5939
ISBN	9783319276663
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-319-27666-3
Links to Related Works	Subject References: Abstract Harmonic Analysis . Dynamical systems and ergodic theory . Dynamics . Ergodic theory . Harmonic analysis . Hyperbolic Geometry . Mathematics . Authors: Bergeron, Nicolas . Corporate Authors: SpringerLink (Online service) . Series: Universitext . Classification: 516.9 .

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The Spectrum of Hyperbolic Surfaces

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