English

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 QQ-Cantor series expansions. In particular, we show that there exists a QQ such that the set of real numbers which are QQ-normal but not QQ-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}
}

Comments

12 pages