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 | |
| Publication status | Published - 8 Nov 2014 |
| Externally published | Yes |
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Keywords
- Addition formulae
- Elliptic curves
- Elliptic functions
- Weierstrass p-function
ASJC Scopus subject areas
- Mathematics(all)
- Engineering(all)
- Physics and Astronomy(all)
Cite this
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
}
TY - JOUR
T1 - Some new addition formulae for Weierstrass elliptic functions
AU - Eilbeck, J. Chris
AU - England, Matthew
AU - Ônishi, Yoshihiro
PY - 2014/11/8
Y1 - 2014/11/8
N2 - 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.
AB - 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.
KW - Addition formulae
KW - Elliptic curves
KW - Elliptic functions
KW - Weierstrass p-function
U2 - 10.1098/rspa.2014.0051
DO - 10.1098/rspa.2014.0051
M3 - Article
VL - 470
JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
SN - 0080-4630
IS - 2171
M1 - 20140051
ER -