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Some New Addition Formulae for Weierstrass Elliptic Functions


Reference:

England, M., Eilbeck, J. C. and Onishi, Y., 2014. Forthcoming. Some New Addition Formulae for Weierstrass Elliptic Functions. Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences, 470 (2171), 20140051.

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    Official URL:

    http://dx.doi.org/10.1098/rspa.2014.0051

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    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 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.

    Details

    Item Type Articles
    CreatorsEngland, M., Eilbeck, J. C. and Onishi, Y.
    DOI10.1098/rspa.2014.0051
    Related URLs
    URLURL Type
    http://arxiv.org/abs/1207.6274Free Full-text
    http://rspa.royalsocietypublishing.org/Publisher
    Uncontrolled Keywordselliptic functions, addition formulae
    DepartmentsFaculty of Science > Computer Science
    RefereedYes
    StatusIn Press
    ID Code30743

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