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

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