Sigma, tau and Abelian functions of algebraic curves

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

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22 Citations (Scopus)


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 languageEnglish
Article number455216
JournalJournal of Physics A: Mathematical and Theoretical
Issue number45
Publication statusPublished - 12 Nov 2010


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