Normality preserving operations for Cantor series expansions and associated fractals part II
Number Theory
2014-07-16 v2
Abstract
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 such that the set of real numbers which are -normal but not -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.
Keywords
Cite
@article{arxiv.1407.0778,
title = {Normality preserving operations for Cantor series expansions and associated fractals part II},
author = {Dylan Airey and Bill Mance and Joseph Vandehey},
journal= {arXiv preprint arXiv:1407.0778},
year = {2014}
}
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12 pages