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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:559616 |
| Date | January 2012 |
| Creators | Blann, Thomas |
| Publisher | University of Nottingham |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://eprints.nottingham.ac.uk/12546/ |
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