Continued fraction normality is not preserved along arithmetic progressions

DOI10.1007/s00013-016-0885-3zbMath1337.11047arXiv1509.05501OpenAlexW2963375018MaRDI QIDQ267053

Byron Heersink, Joseph Vandehey

Publication date: 7 April 2016

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.05501

zbMATH Keywords

normal numberscontinued fractionstransfer operator

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) Continued fractions and generalizations (11J70) Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. (11K16) Metric theory of continued fractions (11K50)

Related Items (4)

Normality of different orders for Cantor series expansions ⋮ Preservation of normality by non-oblivious group selection ⋮ An analogue of Pillai's theorem for continued fraction normality and an application to subsequences ⋮ Some complexity results in the theory of normal numbers

Cites Work

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• Normality and automata
• Subsequences of normal sequences
• Normal numbers and selection rules
• Non literal transducers and some problems of normality
• Generic sequences, transducers and multiplication of normal numbers
• Normal numbers and finite automata
• Selection functions that do not preserve normality
• On the theorem of Gauss-Kusmin-Lévy and a Frobenius-type theorem for function spaces
• Non-trivial matrix actions preserve normality for continued fractions

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