TY - JOUR
T1 - Some new addition formulae for Weierstrass elliptic functions
AU - Eilbeck, J. Chris
AU - England, Matthew
AU - Onishi, Yoshihiro
PY - 2014/9/3
Y1 - 2014/9/3
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 specialisation of the results here. The new formulae, and the techniques used to find them, also follow the recent work for the generalisation 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 specialisation of the results here. The new formulae, and the techniques used to find them, also follow the recent work for the generalisation of Weierstrass' functions to curves of higher genus.
KW - elliptic functions
KW - addition formulae
UR - http://arxiv.org/abs/1207.6274
UR - http://dx.doi.org/10.1098/rspa.2014.0051
UR - http://rspa.royalsocietypublishing.org/
U2 - 10.1098/rspa.2014.0051
DO - 10.1098/rspa.2014.0051
M3 - Article
SN - 1364-5021
VL - 470
JO - Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences
JF - Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences
IS - 2171
M1 - 20140051
ER -