Building Abelian functions with generalised Baker-Hirota operators

Matthew England, Chris Athorne

Research output: Contribution to journalArticle

2 Citations (Scopus)
8 Downloads (Pure)

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.

Original languageEnglish
Article number037
Number of pages36
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume8
DOIs
Publication statusPublished - 26 Jun 2012
Externally publishedYes

Bibliographical note

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Keywords

  • Abelian function
  • Baker-hirota operator
  • Kleinian function
  • R-function

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Mathematical Physics

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