### Abstract

We compare and contrast three different methods for the construction of the differential relations satisfied by the fundamental Abelian functions associated with an algebraic curve. We realize these Abelian functions as logarithmic derivatives of the associated sigma function. In two of the methods, the use of the tau function, expressed in terms of the sigma function, is central to the construction of differential relations between the Abelian functions. © 2010 IOP Publishing Ltd.

Original language | English |
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Article number | 455216 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 43 |

Issue number | 45 |

DOIs | |

Publication status | Published - 12 Nov 2010 |

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## Cite this

Eilbeck, J. C., Enolski, V. Z., & Gibbons, J. (2010). Sigma, tau and Abelian functions of algebraic curves.

*Journal of Physics A: Mathematical and Theoretical*,*43*(45), [455216]. https://doi.org/10.1088/1751-8113/43/45/455216