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Abelian functions associated with genus three algebraic curves

Published online by Cambridge University Press:  01 November 2011

J. C. Eilbeck
Affiliation:
Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, United Kingdom (email: j.c.eilbeck@hw.ac.uk)
M. England
Affiliation:
School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QQ, United Kingdom (email: matthew.england@glasgow.ac.uk)
Y. Ônishi
Affiliation:
Faculty of Education and Human Sciences, University of Yamanashi, 4-3-11, Takeda, Kofu, 400-8511, Japan (email: yonishi@yamanashi.ac.jp)

Abstract

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We develop the theory of Abelian functions associated with algebraic curves. The growth in computer power and the advancement of efficient symbolic computation techniques have allowed for recent progress in this area. In this paper we focus on the genus three cases, comparing the two canonical classes of hyperelliptic and trigonal curves. We present new addition formulae, derive bases for the spaces of Abelian functions and discuss the differential equations such functions satisfy.

Supplementary materials are available with this article.

Type
Research Article
Copyright
Copyright © London Mathematical Society 2011

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