Deriving bases for Abelian functions

England, M. (2011) Deriving bases for Abelian functions. Computational Methods and Function Theory, 11(2), pp. 617-654.

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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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: England, Dr Matthew
• Authors: England, M.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Research Group: ISMP
• Journal Name: Computational Methods and Function Theory
• Journal Abbr.: CMFT
• ISSN: 1617-9447
• Published Online: 24 August 2011

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