Hausdorff dimensions in Pierce expansions
Volume 215 / 2024
Acta Arithmetica 215 (2024), 115-160
MSC: Primary 11K55; Secondary 28A80
DOI: 10.4064/aa230427-18-3
Published online: 22 July 2024
Abstract
The digits of the Pierce expansion obey the law of large numbers, the central limit theorem, and the law of the iterated logarithm in the Lebesgue measure sense. We calculate the Hausdorff dimensions of the exceptional sets associated with each of the three laws. We further determine the Hausdorff dimensions of certain sets arising in Pierce expansions.
