Deriving bases for Abelian functions

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We present a new method to explicitly define Abelian functions associated with algebraic curves, for the purpose of finding bases for the relevant vector spaces of such functions. We demonstrate the procedure with the functions associated with a trigonal curve of genus four. The main motivation for the construction of such bases is that it allows systematic methods for the derivation of the addition formulae and differential equations satisfied by the functions. We present a new 3-term 2-variable addition formulae and a complete set of differential equations to generalise the classic Weierstrass identities for the case of the trigonal curve of genus four.

Original languageEnglish
Pages (from-to)617-654
Number of pages38
JournalComputational Methods and Function Theory
Issue number2
Publication statusPublished - Jan 2012
Externally publishedYes

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DOI 10.1007/BF03321878


  • Abelian functions
  • Addition formula
  • Kleinian sigma-functions
  • P-functions
  • Trigonal curves
  • Weier-strass functions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Computational Theory and Mathematics


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