On the Hausdorff dimension of some sets of numbers defined through the digits of their $Q$-Cantor series expansions

Dylan Airey; Bill Mance

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arXiv · 1407.0776

On the Hausdorff dimension of some sets of numbers defined through the digits of their $Q$-Cantor series expansions

Dylan Airey·Bill Mance

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Abstract

Following in the footsteps of P. Erdős and A. Rényi we compute the Hausdorff dimension of sets of numbers whose digits with respect to their $Q$-Cantor series expansions satisfy various statistical properties. In particular, we consider difference sets associated with various notions of normality and sets of numbers with a prescribed range of digits.

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Dylan Airey, Bill Mance. 2014-07-15. On the Hausdorff dimension of some sets of numbers defined through the digits of their $Q$-Cantor series expansions. https://arxiv.org/abs/1407.0776

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