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...

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Bibliographic Details
Main Author: Blann, Thomas
Format: Thesis (University of Nottingham only)
Language:English
Published: 2012
Online Access:https://eprints.nottingham.ac.uk/12546/
Description
Summary: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.