Crucifix, F.;
(2011)
Some applications of the spectral theory of automorphic forms.
Masters thesis , UCL (University College London).
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Abstract
The thesis gives an overview of several aspects of analytic number theory and spectral theory. The topics presented are seemingly unrelated at first glance. However, as further chapters reveal, underlying each is the spectral theory of automorphic forms. While the material is mostly expository, a few parts are original. These include a new Poincare series that may shed light on the value distribution of multiplier systems, and an explanation of how general results of Anton Good on correlation functions of elements in Fuchsian groups can be applied to give information about Farey fractions. Along the way, the author introduces several fundamental techniques in analytic number theory, such as Weyl's criterion for equidistribution and the Wiener-Ikehara tauberian theory.
| Type: | Thesis (Masters) |
|---|---|
| Title: | Some applications of the spectral theory of automorphic forms |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1317739 |
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