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Higher Genus Abelian Functions Associated with Cyclic Trigonal Curves
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
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Higher Genus Abelian Functions Associated with Cyclic Trigonal Curves
Інший ID:
2010 Mathematics Subject Classification: 33E05; 14H40; 14H42
DOI:10.3842/SIGMA.2010.025
DOI:10.3842/SIGMA.2010.025
Посилання:
Higher Genus Abelian Functions Associated with Cyclic Trigonal Curves / M. England // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 15 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the Eighth International Conference “Symmetry in Nonlinear Mathematical Physics” (June 21–27, 2009, Kyiv, Ukraine). The full collection is available at http://www.emis.de/journals/SIGMA/symmetry2009.html.
Many thanks to Professor Chris Eilbeck for useful conversations. Thanks also to the three
anonymous referees who gave constructive and useful comments.
Дата:
2010
Переглядів:
473
Завантажень:
238
Анотація:
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.
