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

Abstract

We investigate how non-zero rational multiplication and rational addition affect normality with respect to $Q$-Cantor series expansions. In particular, we show that there exists a $Q$ such that the set of real numbers which are $Q$-normal but not $Q$-distribution normal, and which still have this property when multiplied and added by rational numbers has full Hausdorff dimension. Moreover, we give such a number that is explicit in the sense that it is computable.

12 pages

References in corpus (1)

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

Cited by in corpus (1)

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