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Symmetry, Integrability and Geometry: Methods and Applications, 2012, Volume 8, 037, 36 pp.
DOI: https://doi.org/10.3842/SIGMA.2012.037
(Mi sigma714)
 

This article is cited in 2 scientific papers (total in 2 papers)

Building Abelian functions with generalised Baker–Hirota operators

Matthew Englanda, Chris Athorneb

a Department of Computer Science, University of Bath, Bath, BA2 7AY, UK
b School of Mathematics and Statistics, University of Glasgow, G12 8QQ, UK
Full-text PDF (554 kB) Citations (2)
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Abstract: 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.
Received: March 16, 2012; in final form June 18, 2012; Published online June 26, 2012
Bibliographic databases:
Document Type: Article
MSC: 14H40; 14H50; 14H70
Language: English
Citation: Matthew England, Chris Athorne, “Building Abelian functions with generalised Baker–Hirota operators”, SIGMA, 8 (2012), 037, 36 pp.
Citation in format AMSBIB
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\by Matthew England, Chris Athorne
\paper Building Abelian functions with generalised Baker--Hirota operators
\jour SIGMA
\yr 2012
\vol 8
\papernumber 037
\totalpages 36
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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