On the joint normality of certain digit expansions

2014/08/02 by Joseph Vandehey, Vandehey, Joseph
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #math.DS #math.NT

paper · pdf · doi:10.48550/arxiv.1408.0435

arxiv created 2014/08/02 · arxiv updated 2014/08/05

Abstract

We prove that a point x is normal with respect to an ergodic, number-theoretic transformation T if and only if x is normal with respect to Tⁿ for any n≥ 1. This corrects an erroneous proof of Schweiger. Then, using some insights from Schweiger's original proof, we extend these results, showing for example that a number is normal with respect to the regular continued fraction expansion if and only if it is normal with respect to the odd continued fraction expansion.

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