On the frequency of partial quotients of regular continued fractions
arXiv:0906.3283 · doi:10.1017/S0305004109990235
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.
Accepted by Mathematical Proceedings of the Cambridge Philosophical Society