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Normality preserving operations for Cantor series expansions and associated fractals part II
Dylan Airey, Bill Mance, Joseph Vandehey
We investigate how non-zero rational multiplication and rational addition affect normality with respect to -Cantor series expansions. In particular, we show that there exists a…
On the Hausdorff dimension of some sets of numbers defined through the digits of their -Cantor series expansions
Dylan Airey, Bill Mance
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 -Cantor series expansions satisfy va…
Normality preserving operations for Cantor series expansions and associated fractals part I
Dylan Airey, Bill Mance
It is well known that rational multiplication preserves normality in base . We study related normality preserving operations for the -Cantor series expansions. In particular,…
Unexpected distribution phenomenon resulting from Cantor series expansions
Dylan Airey, Bill Mance
We explore in depth the number theoretic and statistical properties of certain sets of numbers arising from their Cantor series expansions. As a direct consequence of our main theo…