On the Hausdorff dimension of some sets of numbers defined through the digits of their $Q$-Cantor series expansions

Abstract

Following in the footsteps of P. Erdős and A. Rényi we compute the Hausdorff dimension of sets of numbers whose digits with respect to their $Q$-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.

13 pages, 1 figure

References in corpus (1)

• Normality preserving operations for Cantor series expansions and associated fractals part II

Cited by in corpus (1)

• Normality preserving operations for Cantor series expansions and associated fractals part II