Fisher, AM and Zhang, X (2023)

Uniform distribution mod 1 for sequences of ergodic sums and continued fractions

Preprint arXiv:2307.14843 [math.DS]; last accessed August 5, 2023 .

ISSN/ISBN: Not available at this time. DOI: Not available at this time.

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Abstract: We establish a necessary and sufficient condition for a sequence of ergodic sums (i.e. Birkhoff partial sums) to be almost surely uniformly distributed mod 1. Applications are given when the sequence is generated by a Gibbs-Markov map. In particular, we show that for almost every real number, the sequence of denominators of the convergents of its continued fraction expansion satisfies Benford's law.

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Bibtex:
@misc{, title={Uniform distribution mod $1$ for sequences of ergodic sums and continued fractions}, author={Albert M. Fisher and Xuan Zhang}, year={2023}, eprint={2307.14843}, archivePrefix={arXiv}, primaryClass={math.DS} }

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Reference Type: Preprint

Subject Area(s): Analysis, Probability Theory

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