• Badly approximablep-adic integers

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    • Keywords


      Diophantine approximation; p-adic numbers; Hausdorff dimension

    • Abstract


      It is known that thep-adic integers that are badly approximable by rationals form a null set with respect to Haar measure. We define a [0,1]-valued dimension function on thep-adic integers analogous to Hausdorff dimension inR and show that with respect to this function the dimension of the set of badly approximablep-adic integers is 1.

    • Author Affiliations


      A G Abercrombie1

      1. Department of Pure Mathematics, University of Liverpool, P.O. Box 147, Liverpool - L693BX, UK
    • Dates

  • Proceedings – Mathematical Sciences | News

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      Posted on July 25, 2019

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