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010   $a9783319276649
024 7 $a10.1007/978-3-319-27666-3
035   $a(DE-He213)978-3-319-27666-3
035   $a(MiAaPQ)EBC6314107
035   $a(MiAaPQ)EBC5577276
035   $a(Au-PeEL)EBL5577276
035   $a(OCoLC)1066196598
035   $a(CKB)3710000000602302
035   $a(EXLCZ)993710000000602302
100   $a20160219d2016      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 14$aThe Spectrum of Hyperbolic Surfaces /$fby Nicolas Bergeron
205   $a1st ed. 2016.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016.
215   $a1 online resource (XIII, 370 p. 8 illus. in color.) 
225 1 $aUniversitext,$x0172-5939
300   $aIncludes index.
327   $aPreface -- 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.
330   $aThis text is an introduction to the spectral theory of the Laplacian on compact or finite area hyperbolic surfaces. For some of these surfaces, called ?arithmetic hyperbolic surfaces?, the eigenfunctions are of arithmetic nature, and one may use analytic tools as well as powerful methods in number theory to study them. After an introduction to the hyperbolic geometry of surfaces, with a special emphasis on those of arithmetic type, and then an introduction to spectral analytic methods on the Laplace operator on these surfaces, the author develops the analogy between geometry (closed geodesics) and arithmetic (prime numbers) in proving the Selberg trace formula. Along with important number theoretic applications, the author exhibits applications of these tools to the spectral statistics of the Laplacian and the quantum unique ergodicity property. The latter refers to the arithmetic quantum unique ergodicity theorem, recently proved by Elon Lindenstrauss. The fruit of several graduate level courses at Orsay and Jussieu, The Spectrum of Hyperbolic Surfaces allows the reader to review an array of classical results and then to be led towards very active areas in modern mathematics.
410  0$aUniversitext,$x0172-5939
606   $aGeometry, Hyperbolic
606   $aHarmonic analysis
606   $aDynamics
606   $aErgodic theory
606   $aHyperbolic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21030
606   $aAbstract Harmonic Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12015
606   $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X
615  0$aGeometry, Hyperbolic.
615  0$aHarmonic analysis.
615  0$aDynamics.
615  0$aErgodic theory.
615 14$aHyperbolic Geometry.
615 24$aAbstract Harmonic Analysis.
615 24$aDynamical Systems and Ergodic Theory.
676   $a516.9
700   $aBergeron$b Nicolas$4aut$4http://id.loc.gov/vocabulary/relators/aut$0756115
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
912   $a9910254081403321
996   $aSpectre des surfaces hyperboliques$91523691
997   $aUNINA