Approximation lattices of p-adic numbers

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    Abstract

    Approximation lattices occur in a natural way in the study of rational approximations to p-adic numbers. Periodicity of a sequence of approximation lattices is shown to occur for rational and quadratic p-adic numbers, and for those only, thus establishing a p-adic analogue of Lagrange's theorem on periodic continued fractions. Using approximation lattices we derive upper and lower bounds for the best approximations to a p-adic number, thus establishing the p-adic analogue of a theorem of Hurwitz.
    Original languageEnglish
    Pages (from-to)70-88
    Number of pages19
    JournalJournal of Number Theory
    Volume24
    Issue number1
    DOIs
    Publication statusPublished - 1986

    Fingerprint

    P-adic numbers
    P-adic
    Approximation
    Lagrange's theorem
    Analogue
    Rational Approximation
    Continued fraction
    Best Approximation
    Periodicity
    Upper and Lower Bounds
    Theorem

    Cite this

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    title = "Approximation lattices of p-adic numbers",
    abstract = "Approximation lattices occur in a natural way in the study of rational approximations to p-adic numbers. Periodicity of a sequence of approximation lattices is shown to occur for rational and quadratic p-adic numbers, and for those only, thus establishing a p-adic analogue of Lagrange's theorem on periodic continued fractions. Using approximation lattices we derive upper and lower bounds for the best approximations to a p-adic number, thus establishing the p-adic analogue of a theorem of Hurwitz.",
    author = "{Weger, de}, B.M.M.",
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    Approximation lattices of p-adic numbers. / Weger, de, B.M.M.

    In: Journal of Number Theory, Vol. 24, No. 1, 1986, p. 70-88.

    Research output: Contribution to journalArticleAcademicpeer-review

    TY - JOUR

    T1 - Approximation lattices of p-adic numbers

    AU - Weger, de, B.M.M.

    PY - 1986

    Y1 - 1986

    N2 - Approximation lattices occur in a natural way in the study of rational approximations to p-adic numbers. Periodicity of a sequence of approximation lattices is shown to occur for rational and quadratic p-adic numbers, and for those only, thus establishing a p-adic analogue of Lagrange's theorem on periodic continued fractions. Using approximation lattices we derive upper and lower bounds for the best approximations to a p-adic number, thus establishing the p-adic analogue of a theorem of Hurwitz.

    AB - Approximation lattices occur in a natural way in the study of rational approximations to p-adic numbers. Periodicity of a sequence of approximation lattices is shown to occur for rational and quadratic p-adic numbers, and for those only, thus establishing a p-adic analogue of Lagrange's theorem on periodic continued fractions. Using approximation lattices we derive upper and lower bounds for the best approximations to a p-adic number, thus establishing the p-adic analogue of a theorem of Hurwitz.

    U2 - 10.1016/0022-314X(86)90059-4

    DO - 10.1016/0022-314X(86)90059-4

    M3 - Article

    VL - 24

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    EP - 88

    JO - Journal of Number Theory

    JF - Journal of Number Theory

    SN - 0022-314X

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    ER -