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arXiv · 1702.04072

On absolutely normal numbers and their discrepancy estimate

Verónica Becher·Adrian-Maria Scheerer·Theodore Slaman
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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.

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Verónica Becher, Adrian-Maria Scheerer, Theodore Slaman. 2017-02-14. On absolutely normal numbers and their discrepancy estimate. https://arxiv.org/abs/1702.04072

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