Abelian Functions for Trigonal Curves of Genus Three

摘要

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