JournalsjfgVol. 3 , No. 2pp. 163–186

The Hausdorff dimension of sets of numbers defined by their QQ-Cantor series expansions

  • Dylan Airey

    University of Texas at Austin, USA
  • Bill Mance

    University of North Texas, Denton, USA
The Hausdorff dimension of sets of numbers defined by their $Q$-Cantor series expansions cover
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Abstract

Following in the footsteps of P. Erdős, A. Rényi, and T. Šalát we compute the Hausdorff dimension of sets of numbers whose digits with respect to their QQ-Cantor series expansions satisfy various statistical properties. In particular, we consider difference sets associated with various notions of normality and sets of numbers with a prescribed range of digits.

Cite this article

Dylan Airey, Bill Mance, The Hausdorff dimension of sets of numbers defined by their QQ-Cantor series expansions. J. Fractal Geom. 3 (2016), no. 2 pp. 163–186

DOI 10.4171/JFG/33