Some new addition formulae for Weierstrass elliptic functions

J. Chris Eilbeck, Matthew England, Yoshihiro Onishi

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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.
Original languageEnglish
Article number20140051
Number of pages20
JournalProceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences
Volume470
Issue number2171
DOIs
Publication statusPublished - 3 Sep 2014

Keywords

  • elliptic functions
  • addition formulae

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