Sigma, tau and Abelian functions of algebraic curves

J. C. Eilbeck; V. Z. Enolski; J. Gibbons

doi:10.1088/1751-8113/43/45/455216

Sigma, tau and Abelian functions of algebraic curves

J. C. Eilbeck, V. Z. Enolski, J. Gibbons

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23 Citations (Scopus)

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
Article number	455216
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	43
Issue number	45
DOIs	https://doi.org/10.1088/1751-8113/43/45/455216
Publication status	Published - 12 Nov 2010

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title = "Sigma, tau and Abelian functions of algebraic curves",

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. {\textcopyright} 2010 IOP Publishing Ltd.",

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AU - Gibbons, J.

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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.

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

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VL - 43

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

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Sigma, tau and Abelian functions of algebraic curves

Abstract

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