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arXiv · 1003.4144

Higher Genus Abelian Functions Associated with Cyclic Trigonal Curves

Matthew England
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Abstract

We develop the theory of Abelian functions associated with cyclic trigonal curves by considering two new cases. We investigate curves of genus six and seven and consider whether it is the trigonal nature or the genus which dictates certain areas of the theory. We present solutions to the Jacobi inversion problem, sets of relations between the Abelian function, links to the Boussinesq equation and a new addition formula.

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Matthew England. 2010-03-24. Higher Genus Abelian Functions Associated with Cyclic Trigonal Curves. https://doi.org/10.3842/sigma.2010.025

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