Some new addition formulae for Weierstrass elliptic functions

J. Chris Eilbeck; Matthew England; Yoshihiro Ônishi

doi:10.1098/rspa.2014.0051

Some new addition formulae for Weierstrass elliptic functions

J. Chris Eilbeck, Matthew England, Yoshihiro Ônishi

Research output: Contribution to journal › Article

Abstract

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.

Original language	English
Article number	20140051
Number of pages	14
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	470
Issue number	2171
DOIs	https://doi.org/10.1098/rspa.2014.0051
Publication status	Published - 8 Nov 2014
Externally published	Yes

Fingerprint

Addition formula

Weierstrass Function

elliptic functions

Elliptic function

Weierstrass functions

Curve

Specialization

curves

Elliptic Curves

Genus

Keywords

Addition formulae
Elliptic curves
Elliptic functions
Weierstrass p-function

ASJC Scopus subject areas

Mathematics(all)
Engineering(all)
Physics and Astronomy(all)

Cite this

Eilbeck, J. C., England, M., & Ônishi, Y. (2014). Some new addition formulae for Weierstrass elliptic functions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 470(2171), [20140051]. https://doi.org/10.1098/rspa.2014.0051

Some new addition formulae for Weierstrass elliptic functions. / Eilbeck, J. Chris; England, Matthew; Ônishi, Yoshihiro.

In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 470, No. 2171, 20140051, 08.11.2014.

Research output: Contribution to journal › Article

Eilbeck, JC, England, M & Ônishi, Y 2014, 'Some new addition formulae for Weierstrass elliptic functions' Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 470, no. 2171, 20140051. https://doi.org/10.1098/rspa.2014.0051

Eilbeck JC, England M, Ônishi Y. Some new addition formulae for Weierstrass elliptic functions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2014 Nov 8;470(2171). 20140051. https://doi.org/10.1098/rspa.2014.0051

Eilbeck, J. Chris ; England, Matthew ; Ônishi, Yoshihiro. / Some new addition formulae for Weierstrass elliptic functions. In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2014 ; Vol. 470, No. 2171.

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Access to Document

10.1098/rspa.2014.0051