On the construction of absolutely normal numbers

Christoph Aistleitner, Adrian-Maria Scheerer, Veronica Becher, Theodore Slaman

Research output: Contribution to journalArticlepeer-review


We give a construction of an absolutely normal real number x such that for every integer b≥2, the discrepancy of the first N terms of the sequence (bnxmod1)n≥0 is of asymptotic order O(N−1/2). This is below the order of discrepancy which holds for almost all real numbers. Even the existence of absolutely normal numbers having a discrepancy of such a small asymptotic order has not been known before.
Original languageEnglish
Pages (from-to)333-346
JournalActa Arithmetica
Issue number4
Publication statusPublished - 2017


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