Somos sequences, continued fractions, and hyperelliptic curves

Alfred J. van der Poorten

    Research output: Contribution to journalConference paper

    Abstract

    I detail the continued fraction expansion of the square root of a monic polynomials of even degree. In the quartic and sextic cases I observe explicitly that parameters appearing in the continued fraction expansion yield integer sequences defined by relations instancing sequences of Somos type. Because each step in the expansion corresponds to addition by the divisor at infinity on (the Jacobian of) the relevant curve I recover the link between Somos sequences and the $mathrm{c}$ -ordinates of the multiples of a point on certain curves.
    Original languageEnglish
    Pages (from-to)98-107
    Number of pages10
    JournalProceedings of the RIMS symposium “Analytic Number Theory and Surrounding Areas”
    Publication statusPublished - 2006
    EventAnalytic Number Theory and Surrounding Areas - Kyoto
    Duration: 18 Oct 200422 Oct 2004

    Keywords

    • continued fraction expansion
    • function field of characteristic zero
    • hyperelliptic curve
    • Somos sequence

    Fingerprint Dive into the research topics of 'Somos sequences, continued fractions, and hyperelliptic curves'. Together they form a unique fingerprint.

    Cite this