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Building Abelian functions with generalised Baker–Hirota operators
Symmetry, integrability and geometry: methods and applications, Tome 8 (2012) Cet article a éte moissonné depuis la source Math-Net.Ru

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We present a new systematic method to construct Abelian functions on Jacobian varieties of plane, algebraic curves. The main tool used is a symmetric generalisation of the bilinear operator defined in the work of Baker and Hirota. We give explicit formulae for the multiple applications of the operators, use them to define infinite sequences of Abelian functions of a prescribed pole structure and deduce the key properties of these functions. We apply the theory on the two canonical curves of genus three, presenting new explicit examples of vector space bases of Abelian functions. These reveal previously unseen similarities between the theories of functions associated to curves of the same genus.
Keywords: Baker–Hirota operator, $\mathcal R$-function, Abelian function, Kleinian function. 
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     author = {Matthew England and Chris Athorne},
     title = {Building {Abelian} functions with generalised {Baker{\textendash}Hirota} operators},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a36/}
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Matthew England; Chris Athorne. Building Abelian functions with generalised Baker–Hirota operators. Symmetry, integrability and geometry: methods and applications, Tome 8 (2012). http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a36/

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