Uniform distribution mod $1$ for sequences of ergodic sums and continued fractions
Dynamical Systems
2025-03-03 v2
Abstract
We establish a coboundary condition for a sequence of ergodic sums (i.e.~Birkhoff partial sums) to be almost surely uniformly distributed mod . 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.
Keywords
Cite
@article{arxiv.2307.14843,
title = {Uniform distribution mod $1$ for sequences of ergodic sums and continued fractions},
author = {Albert M. Fisher and Xuan Zhang},
journal= {arXiv preprint arXiv:2307.14843},
year = {2025}
}