On the Frequency of Partial Quotients of Regular Continued Fractions

نویسندگان

  • AI-HUA FAN
  • LING-MIN LIAO
چکیده

We consider sets of real numbers in [0, 1) with prescribed frequencies of partial quotients in their regular continued fraction expansions. It is shown that the Hausdorff dimensions of these sets, always bounded from below by 1/2, are given by a modified variational principle.

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تاریخ انتشار 2009