• Badly approximablep-adic integers

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      https://www.ias.ac.in/article/fulltext/pmsc/105/02/0123-0134

    • 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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