Some new addition formulae for Weierstrass elliptic functions

We present new addition formulae for the Weierstrass functions associated with a general elliptic curve. We prove the structure of the formulae in n-variables and give the explicit addition formulae for the 2- and 3-variable cases. These new results were inspired by new addition formulae found in th...

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Bibliographic Details
Published in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2014-11, Vol.470 (2171), p.20140051-20140051
Main Authors: Eilbeck, J. Chris, England, Matthew, Ônishi, Yoshihiro
Format: Article
Language:English
Subjects:
Addition Formulae
Elliptic Curves
Elliptic Functions
Weierstrass ℘-Function
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Summary:We present new addition formulae for the Weierstrass functions associated with a general elliptic curve. We prove the structure of the formulae in n-variables and give the explicit addition formulae for the 2- and 3-variable cases. These new results were inspired by new addition formulae found in the case of an equianharmonic curve, which we can now observe as a specialization of the results here. The new formulae, and the techniques used to find them, also follow the recent work for the generalization of Weierstrass functions to curves of higher genus.
ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.2014.0051