Deriving bases for Abelian functions

Research output: Contribution to journalArticle

4 Citations (Scopus)
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Abstract

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
Volume11
Issue number2
DOIs
Publication statusPublished - Jan 2012
Externally publishedYes

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Addition formula
Genus
Differential equations
Differential equation
Curve
Algebraic curve
Vector spaces
Vector space
Generalise
Term
Demonstrate

Bibliographical note

Copyright © and Moral Rights are retained by the author(s) and/ or other copyright
owners. A copy can be downloaded for personal non-commercial research or study,
without prior permission or charge. This item cannot be reproduced or quoted extensively
from without first obtaining permission in writing from the copyright holder(s). The
content must not be changed in any way or sold commercially in any format or medium
without the formal permission of the copyright holders.

DOI 10.1007/BF03321878

Keywords

  • 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

Cite this

Deriving bases for Abelian functions. / England, Matthew.

In: Computational Methods and Function Theory, Vol. 11, No. 2, 01.2012, p. 617-654.

Research output: Contribution to journalArticle

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