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On the frequency of partial quotients of regular continued fractions

Published online by Cambridge University Press:  04 August 2009

AI-HUA FAN ,
LINGMIN LIAO  and
JI-HUA MA
AI-HUA FAN
Affiliation:
LAMFA UMR 6140, CNRS, Université de Picardie Jules Verne, 33, Rue Saint Leu, 80039 Amiens Cedex 1, France. and Department of Mathematics, Wuhan University, Wuhan 430072, China. e-mail: ai-hua.fan@u-picardie.frlingmin.liao@lmpt.univ-tours.frjhma@whu.edu.cn
LINGMIN LIAO
Affiliation:
LAMFA UMR 6140, CNRS, Université de Picardie Jules Verne, 33, Rue Saint Leu, 80039 Amiens Cedex 1, France. and Department of Mathematics, Wuhan University, Wuhan 430072, China. e-mail: ai-hua.fan@u-picardie.frlingmin.liao@lmpt.univ-tours.frjhma@whu.edu.cn
JI-HUA MA
Affiliation:
LAMFA UMR 6140, CNRS, Université de Picardie Jules Verne, 33, Rue Saint Leu, 80039 Amiens Cedex 1, France. and Department of Mathematics, Wuhan University, Wuhan 430072, China. e-mail: ai-hua.fan@u-picardie.frlingmin.liao@lmpt.univ-tours.frjhma@whu.edu.cn
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 148 , Issue 1 , January 2010 , pp. 179 - 192
Copyright
Copyright © Cambridge Philosophical Society 2009

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References

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