The dimensions of spaces of holomorphic second-order cusp forms with characters

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Blann, Thomas (2012) The dimensions of spaces of holomorphic second-order cusp forms with characters. PhD thesis, University of Nottingham.

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Abstract

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.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Diamantis, N.
Wuthrich, C.
Subjects: Q Science > QA Mathematics > QA299 Analysis
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 12546
Depositing User: EP, Services
Date Deposited: 05 Oct 2012 09:50
Last Modified: 15 Dec 2017 05:27
URI: https://eprints.nottingham.ac.uk/id/eprint/12546

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