Building Abelian functions with Baker-Hirota operators

England, M. and Athorne, C. (2012) Building Abelian functions with Baker-Hirota operators. Symmetry, Integrability and Geometry: Methods and Applications, 8(037), pp. 1-36. (doi:10.3842/SIGMA.2012.037)

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Abstract

We consider symmetric generalisations of Hirota's bilinear operator. We demonstrate some of the properties of these operators, focusing on how they may be used to build new classes of Abelian (multiply periodic) functions. We give explicit formulae for the multiple applications of the operators, define infinite sequences of Abelian functions of a given pole structure and deduce some of their properties. We present several explicit examples of vector space bases for Abelian functions obtained using the new results, revealing previously unseen similarities between the bases of functions associated to curves of the same genus.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Athorne, Dr Chris and England, Dr Matthew
Authors: England, M., and Athorne, C.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Symmetry, Integrability and Geometry: Methods and Applications
Journal Abbr.:SIGMA
ISSN:1815-0659
ISSN (Online):1815-0659
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