Abelian Functions for Trigonal Curves of Genus Three

By J. C. Eilbeck, V. Enolski, Shigeki Matsutani, Yoshihiro Ônishi, Emma Previato. 2006

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We develop the theory of generalized Weierstrass sigma- and \wp-functions defined on a trigonal curve of genus three. In particular we give a list of the associated partial differential equations satisfied by the \wp-functions, a proof that the coefficients of the power series expansion of the sigma-function are polynomials of moduli parameters, and the derivation of two addition formulae.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

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