Higher genus Abelian functions associated with cyclic trigonal curves

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6 Citations (Scopus)

Abstract

We develop the theory of Abelian functions associated with cyclic trigonal curves by considering two new cases. We investigate curves of genus six and seven and consider whether it is the trigonal nature or the genus which dictates certain areas of the theory. We present solutions to the Jacobi inversion problem, sets of relations between the Abelian function, links to the Boussinesq equation and a new addition formula.

Original languageEnglish
Article number025
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume6
DOIs
Publication statusPublished - 2010
Externally publishedYes

Keywords

  • Abelian function
  • Cyclic trigonal curve
  • Jacobi inversion problem
  • Kleinian sigma function

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Mathematical Physics

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