Hyperelliptic curves, continued fractions, and Somos sequences

Alfred J. van der Poorten

    Research output: Chapter in Book/Report/Conference proceedingConference proceeding contribution

    Abstract

    We detail the continued fraction expansion of the square root of a monic polynomials of even degree. We note that each step of the expansion corresponds to addition of the divisor at infinity, and interpret the data yielded by the general expansion. In the quartic and sextic cases we observe explicitly that the parameters appearing in the continued fraction expansion yield integer sequences defined by bilinear relations instancing sequences of Somos type.
    Original languageEnglish
    Title of host publicationDynamics & stochastics
    Subtitle of host publicationfestschrift in Honour of M.S. Keane
    EditorsDee Denteneer, Frank den Hollander, Evgeny Verbitskiy
    Place of PublicationBeachwood, Ohio
    PublisherInstitute of Mathematical Statistics
    Pages212-224
    Number of pages13
    ISBN (Print)0940600641
    DOIs
    Publication statusPublished - 2006
    EventWorkshop on Dynamical systems, Probability theory, and Statistical Mehanics - Eindhoven, Netherlands
    Duration: 3 Jan 20057 Jan 2005

    Publication series

    NameLecture notes-monograph series
    PublisherInstitute of Mathematical Statistics
    Volume48

    Workshop

    WorkshopWorkshop on Dynamical systems, Probability theory, and Statistical Mehanics
    CityEindhoven, Netherlands
    Period3/01/057/01/05

    Keywords

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

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  • Cite this

    van der Poorten, A. J. (2006). Hyperelliptic curves, continued fractions, and Somos sequences. In D. Denteneer, F. den Hollander, & E. Verbitskiy (Eds.), Dynamics & stochastics: festschrift in Honour of M.S. Keane (pp. 212-224). (Lecture notes-monograph series; Vol. 48). Beachwood, Ohio: Institute of Mathematical Statistics. https://doi.org/10.1214/074921706000000239