Products of Eisenstein series, their L-functions, and Eichler cohomology for arbitrary real weights
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...
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
| Published: |
2016
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| Online Access: | https://eprints.nottingham.ac.uk/31540/ |
| _version_ | 1848794223039479808 |
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| author | Neururer, Michael |
| author_facet | Neururer, Michael |
| author_sort | Neururer, Michael |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:12:46Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-31540 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T19:12:46Z |
| publishDate | 2016 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-315402025-02-28T11:46:19Z https://eprints.nottingham.ac.uk/31540/ Products of Eisenstein series, their L-functions, and Eichler cohomology for arbitrary real weights Neururer, Michael 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. 2016-03-15 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en arr https://eprints.nottingham.ac.uk/31540/1/Thesis.pdf Neururer, Michael (2016) Products of Eisenstein series, their L-functions, and Eichler cohomology for arbitrary real weights. PhD thesis, University of Nottingham. |
| spellingShingle | Neururer, Michael Products of Eisenstein series, their L-functions, and Eichler cohomology for arbitrary real weights |
| title | Products of Eisenstein series, their L-functions, and Eichler cohomology for arbitrary real weights |
| title_full | Products of Eisenstein series, their L-functions, and Eichler cohomology for arbitrary real weights |
| title_fullStr | Products of Eisenstein series, their L-functions, and Eichler cohomology for arbitrary real weights |
| title_full_unstemmed | Products of Eisenstein series, their L-functions, and Eichler cohomology for arbitrary real weights |
| title_short | Products of Eisenstein series, their L-functions, and Eichler cohomology for arbitrary real weights |
| title_sort | products of eisenstein series, their l-functions, and eichler cohomology for arbitrary real weights |
| url | https://eprints.nottingham.ac.uk/31540/ |