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Distribution of frequencies of digits via multifractal analysis

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Author

Summary, in English

We study the Hausdorff dimension of a large class of sets in the real line defined in terms of the distribution of frequencies of digits for the representation in some integer base. In particular, our results unify and extend classical work of Borel, Besicovitch, Eggleston, and Billingsley in several directions. Our methods are based on recent results concerning the multifractal analysis of dynamical systems and often allow us to obtain explicit expressions for the Hausdorff dimension. This work is still another illustration of the role that the theory of dynamical systems can play in number theory.

Department/s

Publishing year

2002

Language

English

Pages

410-438

Publication/Series

Journal of Number Theory

Volume

97

Issue

2

Document type

Journal article

Publisher

Academic Press

Topic

  • Mathematics

Keywords

  • multifractal analysis
  • frequencies of digits
  • Hausdorff dimension

Status

Published

Research group

  • Dynamical systems

ISBN/ISSN/Other

  • ISSN: 0022-314X