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dc.rights.licenseCC-BY-NC-ND
dc.contributor.advisorBruggeman, R.W.
dc.contributor.authorDijk, D.J. van
dc.date.accessioned2014-09-24T17:01:00Z
dc.date.available2014-09-24T17:01:00Z
dc.date.issued2014
dc.identifier.urihttps://studenttheses.uu.nl/handle/20.500.12932/18443
dc.description.abstractWe develop a theory of Fourier analysis along closed geodesics of Maass automorphic forms. Maass automorphic forms are (skew-)invariant functions with respect to a Fuchsian group on the upper half-plane that are eigenfunctions of the Laplace-Beltrami operator. These functions arise in the spectral theory of (skew-)invariant functions on the upper half-plane or Riemann surfaces. The Fourier analysis of automorphic forms at interior points and cusps is well-documented, and with a nice result: Any Fourier term of an automorphic form at an interior point or cusp is the multiple of a unique normalized Fourier function, this is called a 'dimension one theorem'. However, this is not possible when working along closed geodesics. In this talk we show that using the reflection in a geodesic a local dimension one theorem can be proven: 'If an automorphic form is (anti-)symmetric with respect to the reflection of a geodesic, then the Fourier term along this geodesic is a multiple of the unique normalized (anti-)symmetric Fourier function'.
dc.description.sponsorshipUtrecht University
dc.format.extent296012
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.titleMaass forms and Fourrier decomposition
dc.type.contentMaster Thesis
dc.rights.accessrightsOpen Access
dc.subject.keywordsMaass forms, Fourrier decomposition, SL2R, automorphic forms
dc.subject.courseuuMathematical Sciences


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