Distribution of frequencies of digits via multifractal analysis
Författare
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.
Avdelning/ar
- Matematik LTH
- Dynamical systems
Publiceringsår
2002
Språk
Engelska
Sidor
410-438
Publikation/Tidskrift/Serie
Journal of Number Theory
Volym
97
Issue
2
Dokumenttyp
Artikel i tidskrift
Förlag
Academic Press
Ämne
- Mathematics
Nyckelord
- multifractal analysis
- frequencies of digits
- Hausdorff dimension
Status
Published
Forskningsgrupp
- Dynamical systems
ISBN/ISSN/Övrigt
- ISSN: 0022-314X