English

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 [0,1)[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 1/21/2, 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