Higher Genus Abelian Functions Associated with Cyclic Trigonal Curves

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 inve...

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Main Author:	Matthew England
Format:	Article
Language:	English
Published:	National Academy of Science of Ukraine 2010-03-01
Series:	Symmetry, Integrability and Geometry: Methods and Applications
Subjects:	Abelian function Kleinian sigma function Jacobi inversion problem cyclic trigonal curve
Online Access:	http://dx.doi.org/10.3842/SIGMA.2010.025

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spelling	doaj-1ed0793cd3ce44b9a678e4c893dcfcb02020-11-24T23:58:57ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592010-03-016025Higher Genus Abelian Functions Associated with Cyclic Trigonal CurvesMatthew EnglandWe 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.http://dx.doi.org/10.3842/SIGMA.2010.025Abelian functionKleinian sigma functionJacobi inversion problemcyclic trigonal curve
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Matthew England
spellingShingle	Matthew England Higher Genus Abelian Functions Associated with Cyclic Trigonal Curves Symmetry, Integrability and Geometry: Methods and Applications Abelian function Kleinian sigma function Jacobi inversion problem cyclic trigonal curve
author_facet	Matthew England
author_sort	Matthew England
title	Higher Genus Abelian Functions Associated with Cyclic Trigonal Curves
title_short	Higher Genus Abelian Functions Associated with Cyclic Trigonal Curves
title_full	Higher Genus Abelian Functions Associated with Cyclic Trigonal Curves
title_fullStr	Higher Genus Abelian Functions Associated with Cyclic Trigonal Curves
title_full_unstemmed	Higher Genus Abelian Functions Associated with Cyclic Trigonal Curves
title_sort	higher genus abelian functions associated with cyclic trigonal curves
publisher	National Academy of Science of Ukraine
series	Symmetry, Integrability and Geometry: Methods and Applications
issn	1815-0659
publishDate	2010-03-01
description	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.
topic	Abelian function Kleinian sigma function Jacobi inversion problem cyclic trigonal curve
url	http://dx.doi.org/10.3842/SIGMA.2010.025
work_keys_str_mv	AT matthewengland highergenusabelianfunctionsassociatedwithcyclictrigonalcurves
_version_	1725448712367374336

Higher Genus Abelian Functions Associated with Cyclic Trigonal Curves

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