Elliptic curves and continued fractions

Alfred J. Van Der Poorten*

*Corresponding author for this work

    Research output: Contribution to journalArticle

    13 Citations (Scopus)

    Abstract

    We detail the continued fraction expansion of the square root of the general monic quartic polynomial, noting that each line of the expansion corresponds to addition of the divisor at infinity. We analyse the data yielded by the general expansion. In that way we obtain "elliptic sequences" satisfying Somos relations. I mention several new results on such sequences. The paper includes a detailed "reminder exposition" on continued fractions of quadratic irrationals in function fields.

    Original languageEnglish
    JournalJournal of Integer Sequences
    Volume8
    Issue number2
    Publication statusPublished - 16 May 2005

    Keywords

    • Continued fraction expansion
    • Elliptic curve
    • Function field of characteristic zero
    • Somos sequence

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