The dimensions of spaces of holomorphic second-order cusp forms with characters
To each pair of characters $(\chi,\psi)$ on a Fuchsian group of the first kind we associate a space of functions generalizing the space of second--order cusp forms. We determine the dimensions of these spaces and construct explicit bases. We separate two cases according to the weight. The first case...
| Main Author: | |
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
| Published: |
2012
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| Online Access: | https://eprints.nottingham.ac.uk/12546/ |
| _version_ | 1848791523682942976 |
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| author | Blann, Thomas |
| author_facet | Blann, Thomas |
| author_sort | Blann, Thomas |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | To each pair of characters $(\chi,\psi)$ on a Fuchsian group of the first kind we associate a space of functions generalizing the space of second--order cusp forms. We determine the dimensions of these spaces and construct explicit bases. We separate two cases according to the weight. The first case deals with weight higher than 2 whilst the second deals with the more complicated case of weight 2.
An application of these results to Percolation Theory is provided in the last section. |
| first_indexed | 2025-11-14T18:29:52Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-12546 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T18:29:52Z |
| publishDate | 2012 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-125462025-02-28T11:19:54Z https://eprints.nottingham.ac.uk/12546/ The dimensions of spaces of holomorphic second-order cusp forms with characters Blann, Thomas To each pair of characters $(\chi,\psi)$ on a Fuchsian group of the first kind we associate a space of functions generalizing the space of second--order cusp forms. We determine the dimensions of these spaces and construct explicit bases. We separate two cases according to the weight. The first case deals with weight higher than 2 whilst the second deals with the more complicated case of weight 2. An application of these results to Percolation Theory is provided in the last section. 2012-07-19 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en arr https://eprints.nottingham.ac.uk/12546/1/Thesis_-_250412.pdf Blann, Thomas (2012) The dimensions of spaces of holomorphic second-order cusp forms with characters. PhD thesis, University of Nottingham. |
| spellingShingle | Blann, Thomas The dimensions of spaces of holomorphic second-order cusp forms with characters |
| title | The dimensions of spaces of holomorphic second-order cusp forms with characters |
| title_full | The dimensions of spaces of holomorphic second-order cusp forms with characters |
| title_fullStr | The dimensions of spaces of holomorphic second-order cusp forms with characters |
| title_full_unstemmed | The dimensions of spaces of holomorphic second-order cusp forms with characters |
| title_short | The dimensions of spaces of holomorphic second-order cusp forms with characters |
| title_sort | dimensions of spaces of holomorphic second-order cusp forms with characters |
| url | https://eprints.nottingham.ac.uk/12546/ |