Some new addition formulae for Weierstrass elliptic functions-Reference-Cited by-同舟云学术

Some new addition formulae for Weierstrass elliptic functions

Published:2014-11-08 Issue:2171 Volume:470 Page:20140051
ISSN:1364-5021
Container-title:Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Proc. R. Soc. A.

Author:

Eilbeck J. Chris¹,England Matthew²,Ônishi Yoshihiro³

Affiliation:

1. Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK

2. Department of Computer Science, University of Bath, Bath BA2 7AY, UK

3. Faculty of Sciences and Technology, Department of Mathematics, Meijo University, 1-501 Shiogamaguchi, Tenpaku-ku, Nagoya 468-8502, Japan

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.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2014.0051

Reference24 articles.

1. Whittaker ET& Watson GN. 1927 A course of modern analysis. 4th edn. Cambridge UK: Cambridge University Press.

2. Addition formulae for Abelian functions associated with specialized curves

3. Buchstaber VM Enolskii VZ& Leykin DV. 1997 Kleinian functions hyperelliptic Jacobians and applications. Rev. Math. Math. Phys. 10 1–125 (For an updated version see http://arxiv.org/abs/1208.0990).

4. On the Kleinian construction of abelian functions of canonical algebraic curves

5. Abelian functions for trigonal curves of genus three;Eilbeck JC;Int. Math. Res. Notices,2008