Spectre des Surfaces Hyperboliques

ISBN-10: 2759805646

ISBN-13: 9782759805648

Edition: 0

Authors: Nicolas Bergeron
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Description: Cet ouvrage est une introduction a la theorie spectrale du laplacien sur les surfaces hyperboliques (de courbure 1), compactes ou d'aire finie. Pour certaines de ces surfaces, dites - surfaces hyperboliques arithmetiques -, les fonctions propres sont des objets de nature arithmetique et des outils d'analyse sont employes conjointement a des methodes puissantes de theorie des nombres pour les etudier. Apres une introduction a la geometrie hyperbolique des surfaces insistant sur celles qui sont arithmetiques, puis une introduction aux methodes d'analyse spectrale de l'operateur de Laplace sur celles- ci, l'auteur developpe l'analogie geometrie (geodesiques fermees) - arithmetique (nombres premiers) en demontrant la formule des traces de Selberg. Outre des applications importantes a l'arithmetique, l'auteur propose des applications a la statistique spectrale de l'operateur de Laplace et a la propriete d'unique ergodicite quantique (theoreme d'unique ergodicite quantique arithmetique, recemment demontre par Elon Lindenstrauss). L'ouvrage, issu de plusieurs cours de M2 a Orsay et a l'Universite P. & M. Curie, permet au lecteur de parcourir un champ mathematique classique et d'etre conduit vers des domaines de recherche tres actifs.

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Book details

List price: $52.00
Copyright year: 0
Publisher: EDP Sciences
Binding: Paperback
Pages: 350
Size: 6.00" wide x 9.00" long x 0.73" tall
Weight: 1.034
Language: English

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