Sigma, tau and Abelian functions of algebraic curves

Details Sigma, tau and Abelian functions of algebraic curves Sigma, tau and Abelian functions of algebraic curves

2010-06-27

arxiv.org/abs/1006.5219v1

J. Phys. A: Math. Theor. 43 (2010) 455216

Mathematics

Algebraic Geometry

25 pages

Scientific paper

10.1088/1751-8113/43/45/455216

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.

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