Heriot-Watt Mathematics Report Series
HWM06-48, 22 Dec 2006

Abelian Functions for Cyclic Trigonal Curves of Genus Four

S Baldwin, JC Eilbeck, J Gibbons and Y Onishi


Abstract

We discuss the theory of generalized Weierstrass $\sigma$ and $\wp$ functions defined on a trigonal curve of genus four, following earlier work on the genus three case. The specific example of the ``purely trigonal'' (or ``cyclic trigonal'') curve $y^3=x^5+\lambda_4 x^4 +\lambda_3 x^3+\lambda_2 x^2 +\lambda_1 x+\lambda_0$ is discussed in detail, including a list of some of the associated partial differential equations satisfied by the $\wp$ functions, and the derivation of an addition formulae.

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Full text: http://uk.arxiv.org/abs/math.AG/0612654


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