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Symmetry, Integrability and Geometry: Methods and Applications, 2010, Volume 6, 025, 22 pp.
DOI: https://doi.org/10.3842/SIGMA.2010.025 (Mi sigma482) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Higher Genus Abelian Functions Associated with Cyclic Trigonal Curves

Matthew England

Department of Mathematics, University of Glasgow, UK
Full-text PDF (322 kB) Citations (7)
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DOI: https://doi.org/10.3842/SIGMA.2010.025
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.
Received: December 31, 2009; in final form March 19, 2010; Published online March 24, 2010
Bibliographic databases:
Document Type: Article
MSC: 33E05; 14H40; 14H42
Language: English
Citation: Matthew England, “Higher Genus Abelian Functions Associated with Cyclic Trigonal Curves”, SIGMA, 6 (2010), 025, 22 pp.
Citation in format AMSBIB
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\paper Higher Genus Abelian Functions Associated with Cyclic Trigonal Curves
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    • This publication is cited in the following 7 articles:
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    		Symmetry, Integrability and Geometry: Methods and Applications
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