dc.rights.license | CC-BY-NC-ND | |
dc.contributor.advisor | Bruggeman, R.W. | |
dc.contributor.author | Dijk, D.J. van | |
dc.date.accessioned | 2014-09-24T17:01:00Z | |
dc.date.available | 2014-09-24T17:01:00Z | |
dc.date.issued | 2014 | |
dc.identifier.uri | https://studenttheses.uu.nl/handle/20.500.12932/18443 | |
dc.description.abstract | We 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.sponsorship | Utrecht University | |
dc.format.extent | 296012 | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en | |
dc.title | Maass forms and Fourrier decomposition | |
dc.type.content | Master Thesis | |
dc.rights.accessrights | Open Access | |
dc.subject.keywords | Maass forms, Fourrier decomposition, SL2R, automorphic forms | |
dc.subject.courseuu | Mathematical Sciences | |