Recurrence relations for elliptic sequences: Every somos 4 is a somos k

Alfred J. Van Der Poorten*, Christine S. Swart

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    21 Citations (Scopus)

    Abstract

    In his celebrated memoir, Morgan Ward's definition of elliptic divisibility sequences has the remarkable feature that it does not become at all clear until deep into the paper that there exist nontrivial examples of such sequences. Even then, Ward's proof of the coherence of his definition relies on displaying a sequence of values of quotients of Weierstraß σ-functions. We give a direct proof of coherence and show, rather more generally, that a sequence defined by a so-called Somos relation of width 4 is always also given by three-term Somos relations of all larger widths 5, 6, 7, . . . .

    Original languageEnglish
    Pages (from-to)546-554
    Number of pages9
    JournalBulletin of the London Mathematical Society
    Volume38
    Issue number4
    DOIs
    Publication statusPublished - Aug 2006

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