Products of Eisenstein series, their L-functions, and Eichler cohomology for arbitrary real weights

Neururer, Michael (2016) Products of Eisenstein series, their L-functions, and Eichler cohomology for arbitrary real weights. PhD thesis, University of Nottingham.

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Abstract

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.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Diamantis, Nikolaos
Subjects: Q Science > QA Mathematics > QA299 Analysis
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 31540
Depositing User: Neururer, Michael
Date Deposited: 08 Aug 2016 14:57
Last Modified: 18 Sep 2016 10:48
URI: http://eprints.nottingham.ac.uk/id/eprint/31540

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