On absolutely normal numbers and their discrepancy estimate

Verónica Becher; Adrian-Maria Scheerer; Theodore Slaman

On absolutely normal numbers and their discrepancy estimate

Number Theory 2017-07-12 v2 Other Computer Science

Authors: Verónica Becher , Adrian-Maria Scheerer , Theodore Slaman

Abstract

We construct the base $2$ expansion of an absolutely normal real number $x$ so that, for every integer $b$ greater than or equal to $2$ , the discrepancy modulo $1$ of the sequence $(b^0 x, b^1 x, b^2 x , \ldots)$ is essentially the same as that realized by almost all real numbers.

Keywords

perfect numbers univoque expansions multiplicative functions

Cite

@article{arxiv.1702.04072,
  title  = {On absolutely normal numbers and their discrepancy estimate},
  author = {Verónica Becher and Adrian-Maria Scheerer and Theodore Slaman},
  journal= {arXiv preprint arXiv:1702.04072},
  year   = {2017}
}

Comments

This paper has been superseded by: "On the construction of absolutely normal numbers" by Christoph Aistleitner, Ver\'onica Becher, Adrian-Maria Scheerer and Theodore Slaman, July 2017, arXiv:1707.02628, http://arxiv.org/abs/1707.02628

On absolutely normal numbers and their discrepancy estimate

Abstract

Keywords

Cite

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