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Selberg and Ruelle zeta functions and the relative analytic torsion on complete odd-dimensional hyperbolic manifolds of finite volume

dc.contributor.advisorMüller, Werner
dc.contributor.authorPfaff, Jonathan
dc.date.accessioned2020-04-18T00:56:35Z
dc.date.available2020-04-18T00:56:35Z
dc.date.issued27.08.2012
dc.identifier.urihttps://hdl.handle.net/20.500.11811/5368
dc.description.abstractLet X be a complete hyperbolic manifold of finite volume and of odd dimension d. Firstly, we study Selberg zeta functions on X, prove that these functions have a meromorphic continuation to the entire complex plane and describe their singularities. Secondly, we define the relative or regularized analytic torsion of X associated to certain representations of its fundamental group. We investigate the asymptotic behaviour of this torsion with respect to special sequences of representations. Finally, if X is 3-dimensional, we establish a relation between the regularized analytic torsion and the behaviour of a twisted Ruelle zeta function at 0. Our work generalizes results of Fried, Bunke and Olbrich, Bröcker and Wotzke to the non-compact case and results of Müller to the non-compact and higher-dimensional situation.en
dc.language.isoeng
dc.rightsIn Copyright
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectSelbergsche Zetafunktion
dc.subjectRuellesche Zetafunktion
dc.subjectAnalytische Torsion
dc.subjectHyperbolische Mannigfaltigkeiten
dc.subjectSelbergsche Spurformel
dc.subject.ddc510 Mathematik
dc.titleSelberg and Ruelle zeta functions and the relative analytic torsion on complete odd-dimensional hyperbolic manifolds of finite volume
dc.typeDissertation oder Habilitation
dc.publisher.nameUniversitäts- und Landesbibliothek Bonn
dc.publisher.locationBonn
dc.rights.accessRightsopenAccess
dc.identifier.urnhttps://nbn-resolving.org/urn:nbn:de:hbz:5n-29533
ulbbn.pubtypeErstveröffentlichung
ulbbnediss.affiliation.nameRheinische Friedrich-Wilhelms-Universität Bonn
ulbbnediss.affiliation.locationBonn
ulbbnediss.thesis.levelDissertation
ulbbnediss.dissID2953
ulbbnediss.date.accepted11.07.2012
ulbbnediss.fakultaetMathematisch-Naturwissenschaftliche Fakultät
dc.contributor.coRefereeHoffmann, Werner


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