This article is cited in 7 papers

Higher Genus Abelian Functions Associated with Cyclic Trigonal Curves

Matthew England

Department of Mathematics, University of Glasgow, UK

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.

Keywords: Abelian function; Kleinian sigma function; Jacobi inversion problem; cyclic trigonal curve.

MSC: 33E05; 14H40; 14H42

Received: December 31, 2009; in final form March 19, 2010; Published online March 24, 2010

Language: English

DOI: 10.3842/SIGMA.2010.025

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ArXiv: 1003.4144