Hausdorff dimensions in Pierce expansions

Autorzy

Dane publikacji

  • DOI: 10.4064/aa230427-18-3

  • Tom 215

  • Zeszyt 2

  • Czasopismo: Acta Arithmetica

  • Strony: 115-160

  • Data publikacji online: 21.07.2024

Liczba wyświetleń: 0

Liczba pobrań: 0

Abstrakt

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.