One topic of this thesis are products of two Eisenstein series. First we investigate the subspaces of modular forms of level N that are generated by such products. We show that of the weight k is greater than 2, for many levels, one can obtain the whole of M[subspace]k(N) from Eisenstein series and products of two Eisenstein series. We also provide a result in the case k=2 and treat some spaces of modular forms of non-trivial nebentypus. We then analyse the L-functions of products of Eisenstein series. We reinterpret a method by Rogers-Zudilin and use it in two applications, the first concerning critical L-values of a product of two Eisenstein series, and the second special values of derivatives of L-functions. The last part of this thesis deals with the theory of Eichler-cohomology for arbitrary real weights, which was first developed by Knopp in 1974. We establish a new approach to Knopp's theory using techniques from the spectal theory of automorphic forms, reprove Knopp's main theorems, and also providea vector-valued version of the theory.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:692719 |
| Date | January 2016 |
| Creators | Neururer, Michael |
| Publisher | University of Nottingham |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://eprints.nottingham.ac.uk/31540/ |
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