### 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

*Journal of Physics A: Mathematical and Theoretical*,

*43*(45), [455216]. https://doi.org/10.1088/1751-8113/43/45/455216

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*Journal of Physics A: Mathematical and Theoretical*, vol. 43, no. 45, 455216. https://doi.org/10.1088/1751-8113/43/45/455216

**Sigma, tau and Abelian functions of algebraic curves.** / Eilbeck, J. C.; Enolski, V. Z.; Gibbons, J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Sigma, tau and Abelian functions of algebraic curves

AU - Eilbeck, J. C.

AU - Enolski, V. Z.

AU - Gibbons, J.

PY - 2010/11/12

Y1 - 2010/11/12

N2 - 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.

AB - 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.

U2 - 10.1088/1751-8113/43/45/455216

DO - 10.1088/1751-8113/43/45/455216

M3 - Article

VL - 43

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 45

M1 - 455216

ER -