## Weierstrass functions for the Trigonal (3,5) curve

This page (currently under construction) is intended to contain
eventually a repository of results referring to Weierstrass theory for
*general* trigonal curves of genus 4
*y*^{3} + (μ_{2} x +μ_{5}) y^{2}
+ (μ_{1}x^{3} + μ_{4}x^{2}
+ μ_{7}x + μ_{10}) y = x^{5} +
μ_{3} x^{4} + μ_{6} x^{3} +
μ_{9} x^{2} + μ_{12}x +
μ_{15}

At the moment the only case that has been considered is the *
Strictly Trigonal* case, written in the form

*y*^{3} = x^{5} + λ_{4} x^{4} +
λ_{3}x^{3} + λ_{2}x^{2} +
λ_{1}x + λ_{0}

See the following paper for details of this theory:

*Abelian Functions for Purely Trigonal Curves of Genus
four* - S. Baldwin, J. C. Eilbeck, J. Gibbons, and
Y. Ônishi, math.AG/0612654,
J. Geom. Phys.,
**58**, 450--467, 2008

Some Maple data files on the (3,5) case we be placed here eventually.

Maintained by Chris Eilbeck/Heriot-Watt University, Edinburgh/
J.C.Eilbeck@hw.ac.uk