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2016•Journal of Fractal Geometry Mathematics of Fractals and Related TopicsRequires access

The Hausdorff dimension of sets of numbers defined by their $Q$-Cantor series expansions

Dylan Airey, Bill Mance

Open publisher page 5 citations

Abstract

Following in the footsteps of P. Erdős, A. Rényi, and T. Šalát 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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What this paper is about

Following in the footsteps of P. Erdős, A. Rényi, and T. Šalát 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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OpenAlex reports 5 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Following in the footsteps of P. Erdős, A. Rényi, and T. Šalát 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.

Key concepts: Hausdorff dimension, Mathematics, Packing dimension, Series (stratigraphy), Minkowski–Bouligand dimension, Dimension (graph theory), Hausdorff measure, Effective dimension

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