Determined sequences, continued fractions, and hyperelliptic curves

Alfred J. Van Der Poorten*

*Corresponding author for this work

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

    Abstract

    In this report I sanitise (in the sense of 'bring some sanity to') the arguments of earlier reports detailing the correspondence between sequences (M + hS)-∞<h<∞ of divisors on elliptic and genus two hyperelliptic curves, the continued fraction expansion of quadratic irrational functions in the relevant elliptic and hyperelliptic function fields, and certain integer sequences satisfying relations of Somos type. I note that one may often readily determine the coefficients in those relations by elementary linear algebra.

    Original languageEnglish
    Title of host publicationAlgorithmic Number Theory - 7th International Symposium, ANTS-VII, Proceedings
    EditorsFlorian Hess, Sebastian Pauli, Michael Pohst
    PublisherSpringer, Springer Nature
    Pages393-405
    Number of pages13
    Volume4076 LNCS
    ISBN (Print)3540360751, 9783540360759
    Publication statusPublished - 2006
    Event7th International Symposium on Algorithmic Number Theory, ANTS-VII - Berlin, Germany
    Duration: 23 Jul 200628 Jul 2006

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume4076 LNCS
    ISSN (Print)03029743
    ISSN (Electronic)16113349

    Other

    Other7th International Symposium on Algorithmic Number Theory, ANTS-VII
    CountryGermany
    CityBerlin
    Period23/07/0628/07/06

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  • Cite this

    Van Der Poorten, A. J. (2006). Determined sequences, continued fractions, and hyperelliptic curves. In F. Hess, S. Pauli, & M. Pohst (Eds.), Algorithmic Number Theory - 7th International Symposium, ANTS-VII, Proceedings (Vol. 4076 LNCS, pp. 393-405). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4076 LNCS). Springer, Springer Nature.