Abelian Functions for Trigonal Curves of Genus Three
J. C. Eilbeck, V. Z. Enolski, S. Matsutani, Y. Ônishi, E. Previato
Abstract
We develop the theory of generalized Weierstrass sigma- and -functions defined on a 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 sigma-function are polynomials of moduli parameters, and the derivation of two addition formulae.
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