uu.seUppsala University Publications
Change search
ReferencesLink to record
Permanent link

Direct link
Automorphic distributions and Selberg zeta functions
Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics.
Manuscript (Other academic)
URN: urn:nbn:se:uu:diva-97336OAI: oai:DiVA.org:uu-97336DiVA: diva2:172227
Available from: 2008-05-19 Created: 2008-05-19 Last updated: 2010-01-13Bibliographically approved
In thesis
1. Studies on boundary values of eigenfunctions on spaces of constant negative curvature
Open this publication in new window or tab >>Studies on boundary values of eigenfunctions on spaces of constant negative curvature
2008 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of two papers on the spectral geometry of locally symmetric spaces of Riemannian and Lorentzian signature. Both works are concerned with the idea of relating analysis on such spaces to structures on their boundaries.

The first paper is motivated by a conjecture of Patterson on the Selberg zeta function of Kleinian groups. We consider geometrically finite hyperbolic cylinders with non-compact Riemann surfaces of finite area as cross sections. For these cylinders, we present a detailed investigation of the Bunke-Olbrich extension operator under the assumption that the cross section of the cylinder has one cusp. We establish the meromorphic continuation of the extension of Eisenstein series and incomplete theta series through the limit set. Furthermore, we derive explicit formulas for the residues of the extension operator in terms of boundary values of automorphic eigenfunctions.

The motivation for the second paper comes from conformal geometry in Lorentzian signature. We prove the existence and uniqueness of a sequence of differential intertwining operators for spherical principal series representations, which are realized on boundaries of anti de Sitter spaces. Algebraically, these operators correspond to homomorphisms of generalized Verma modules. We relate these families to the asymptotics of eigenfunctions on anti de Sitter spaces.

Place, publisher, year, edition, pages
Uppsala: Matematiska institutionen, 2008. vi, 23 p.
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 57
Hyperbolic space, anti de Sitter space, spectral geometry, scattering theory, analysis on real and complex Lie groups, intertwining operators, Verma modules, analysis on homogeneous spaces, conformal differential geometry, Selberg zeta functions
National Category
urn:nbn:se:uu:diva-8920 (URN)978-91-506-2010-8 (ISBN)
Public defence
2008-06-11, Häggsalen, Ångström Laboratory, Lägerhyddsvägen 1, Uppsala, 13:15
Available from: 2008-05-19 Created: 2008-05-19Bibliographically approved

Open Access in DiVA

No full text

By organisation
Department of Mathematics

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 181 hits
ReferencesLink to record
Permanent link

Direct link