Normality preserving operations for Cantor series expansions and associated fractals part I

2014/07/03 by Airey, Dylan, Mance, Bill
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1407.0777

Abstract

It is well known that rational multiplication preserves normality in base b. We study related normality preserving operations for the Q-Cantor series expansions. In particular, we show that while integer multiplication preserves Q-distribution normality, it fails to preserve Q-normality in a particularly strong manner. We also show that Q-distribution normality is not preserved by non-integer rational multiplication on a set of zero measure and full Hausdorff dimension.

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