Some New Addition Formulae for Weierstrass Elliptic Functions

John Christopher Eilbeck, Matthew England, Yoshihiro Ônishi

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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
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2171
Publication statusPublished - 8 Nov 2014


  • math.AG
  • math.NT
  • 11G05 (Primary) 33E05, 14H45, 14H52, 37K20 (Secondary)


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