On the frequency of partial quotients of regular continued fractions
classification
🧮 math.DS
math.NT
keywords
continuedpartialquotientsregularsetsalwaysbelowbounded
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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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