Normal number constructions for Cantor series with slowly growing bases

2014/09/18 by Airey, Dylan, Mance, Bill, Vandehey, Joseph
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1409.5220

Abstract

Let Q=(q_n)_n=1^∞ be a sequence of bases with q_i≥ 2. In the case when the q_i are slowly growing and satisfy some additional weak conditions, we provide a construction of a number whose Q-Cantor series expansion is both Q-normal and Q-distribution normal. Moreover, this construction will result in a computable number provided we have some additional conditions on the computability of Q, and from this construction we can provide computable constructions of numbers with atypical normality properties.

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