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 language | English |
|---|---|
| Pages (from-to) | 617-654 |
| Number of pages | 38 |
| Journal | Computational Methods and Function Theory |
| Volume | 11 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Jan 2012 |
| Externally published | Yes |
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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