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

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 (PhD) Diamantis, N.Wuthrich, C. UK Campuses > Faculty of Science > School of Mathematical Sciences 2546 Dr Thomas Blann 05 Oct 2012 10:50 05 Oct 2012 10:50

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