Abelian Functions for Trigonal Curves of Genus Three
Algebraic Geometry
2007-12-12 v2
Abstract
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.
Keywords
Cite
@article{arxiv.math/0610019,
title = {Abelian Functions for Trigonal Curves of Genus Three},
author = {J. C. Eilbeck and V. Z. Enolski and S. Matsutani and Y. Ônishi and E. Previato},
journal= {arXiv preprint arXiv:math/0610019},
year = {2007}
}
Comments
32 pages, no figures. Revised version has the a fuller description of the general (3,4) trigonal curve results, the first version described only the "Purely Trigonal" case