On the frequency of partial quotients of regular continued fractions
Dynamical Systems
2015-05-13 v1 Number Theory
Abstract
We consider sets of real numbers in 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 , are given by a modified variational principle.
Keywords
Cite
@article{arxiv.0906.3283,
title = {On the frequency of partial quotients of regular continued fractions},
author = {Ai-Hua Fan and Lingmin Liao and Ji-Hua Ma},
journal= {arXiv preprint arXiv:0906.3283},
year = {2015}
}
Comments
Accepted by Mathematical Proceedings of the Cambridge Philosophical Society