On the frequency of partial quotients of regular continued fractions

Details On the frequency of partial quotients of regular continued fractions On the frequency of partial quotients of regular continued fractions

2009-06-17

arxiv.org/abs/0906.3283v1

Mathematics

Dynamical Systems

Accepted by Mathematical Proceedings of the Cambridge Philosophical Society

Scientific paper

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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