Deriving bases for Abelian functions

Details Deriving bases for Abelian functions Deriving bases for Abelian functions

2011-03-02

arxiv.org/abs/1103.0468v2

Comput. Methods Funct. Theory 11:2 (2011) 617-654

Physics

Mathematical Physics

35pages

Scientific paper

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.

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