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 inn-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.
Department of Mathematics and the Maxwell Institute for Mathematical Sciences , Heriot-Watt University , Edinburgh EH14 4AS, UK.
J Chris
JC
Eilbeck
Department of Computer Science , University of Bath , Bath BA2 7AY, UK.
Matthew
M
England
Faculty of Sciences and Technology, Department of Mathematics , Meijo University , 1-501 Shiogamaguchi, Tenpaku-ku, Nagoya 468-8502, Japan.
Yoshihiro
Y
Onishi
Weierstrass ℘-function; addition formulae; elliptic curves; elliptic functions