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

  • Dylan Airey

    University of Texas at Austin, USA
  • Bill Mance

    University of North Texas, Denton, USA

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 -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 -Cantor series expansions. J. Fractal Geom. 3 (2016), no. 2, pp. 163–186

DOI 10.4171/JFG/33