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Abelian Functions for Cyclic Trigonal Curves of Genus Four

Abstract

We discuss the theory of generalized Weierstrass σ\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 y3=x5+λ4x4+λ3x3+λ2x2+λ1x+λ0y^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.Comment: 23 page

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    Last time updated on 31/03/2019