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arXiv · 0906.3283

On the frequency of partial quotients of regular continued fractions

Ai-Hua Fan·Lingmin Liao·Ji-Hua Ma
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Abstract

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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Ai-Hua Fan, Lingmin Liao, Ji-Hua Ma. 2009-06-17. On the frequency of partial quotients of regular continued fractions. https://doi.org/10.1017/s0305004109990235

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