### Abstract

We develop the theory of generalized Weierstrass s- and P-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 P-functions, a proof that the coefficients of the power series expansion of the s-function are polynomials of coefficients of the defining equation of the curve, and the derivation of two addition formulae. © The Author 2007.

Original language | English |
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Article number | rnm140 |

Journal | International Mathematics Research Notices |

Volume | 2007 |

DOIs | |

Publication status | Published - 2007 |

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## Cite this

Eilbeck, J. C., Enolski, V. Z., Matsutani, S., Ônishi, Y., & Previato, E. (2007). Abelian functions for trigonal curves of genus three.

*International Mathematics Research Notices*,*2007*, [rnm140]. https://doi.org/10.1093/imrn/rnm140