Selberg and Ruelle zeta functions on compact hyperbolic odd dimensional manifolds
Selberg and Ruelle zeta functions on compact hyperbolic odd dimensional manifolds
Dokument öffnen (1021.5KB)Art der Hochschulschrift
DissertationPrüfungsdatum
26.10.2015Datum der Veröffentlichung
12.11.2015Erstgutachter
Müller, WernerZweitgutachter
Ballmann, WernerMetadaten
Zur Langanzeige
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Inhalt
In this thesis we study the Selberg and Ruelle zeta functions on compact oriented hyperbolic manifolds
X of odd dimension d. We prove that they converge in some half-plane Re(s)>c and that they admit a meromorphic continuation to the whole complex plane.
We also describe the singularities of the Selberg zeta function in terms of the discrete spectrum of certain differential operators on X.
Furthermore, we provide functional equations relating their values at s with those at −s. The main tool that we use is the Selberg trace formula for non-unitary twists.
X of odd dimension d. We prove that they converge in some half-plane Re(s)>c and that they admit a meromorphic continuation to the whole complex plane.
We also describe the singularities of the Selberg zeta function in terms of the discrete spectrum of certain differential operators on X.
Furthermore, we provide functional equations relating their values at s with those at −s. The main tool that we use is the Selberg trace formula for non-unitary twists.
Klassifikation (DDC)
510 MathematikSpilioti, Polyxeni: Selberg and Ruelle zeta functions on compact hyperbolic odd dimensional manifolds. - Bonn, 2015. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-41976
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-41976
@phdthesis{handle:20.500.11811/6566,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-41976,
author = {{Polyxeni Spilioti}},
title = {Selberg and Ruelle zeta functions on compact hyperbolic odd dimensional manifolds},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2015,
month = nov,
note = {In this thesis we study the Selberg and Ruelle zeta functions on compact oriented hyperbolic manifolds
X of odd dimension d. We prove that they converge in some half-plane Re(s)>c and that they admit a meromorphic continuation to the whole complex plane.
We also describe the singularities of the Selberg zeta function in terms of the discrete spectrum of certain differential operators on X.
Furthermore, we provide functional equations relating their values at s with those at −s. The main tool that we use is the Selberg trace formula for non-unitary twists.},
url = {https://hdl.handle.net/20.500.11811/6566}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-41976,
author = {{Polyxeni Spilioti}},
title = {Selberg and Ruelle zeta functions on compact hyperbolic odd dimensional manifolds},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2015,
month = nov,
note = {In this thesis we study the Selberg and Ruelle zeta functions on compact oriented hyperbolic manifolds
X of odd dimension d. We prove that they converge in some half-plane Re(s)>c and that they admit a meromorphic continuation to the whole complex plane.
We also describe the singularities of the Selberg zeta function in terms of the discrete spectrum of certain differential operators on X.
Furthermore, we provide functional equations relating their values at s with those at −s. The main tool that we use is the Selberg trace formula for non-unitary twists.},
url = {https://hdl.handle.net/20.500.11811/6566}
}
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