Recent progress on pointwise normality of self-similar measures
Dynamical Systems
2025-04-28 v1 Classical Analysis and ODEs
Number Theory
Abstract
This article is an exposition of recent results and methods on the prevalence of normal numbers in the support of self-similar measures on the line. We also provide an essentially self-contained proof of a recent Theorem that the Rajchman property (decay of the Fourier transform) implies that typical elements in the support of the measure are normal to all bases; as no decay rate is required, this improves the classical criterion of Davenport, Erdos, and LeVeque (1964). Open problems regarding effective equidistribution, non-integer bases, and higher order correlations, are discussed.
Cite
@article{arxiv.2504.18192,
title = {Recent progress on pointwise normality of self-similar measures},
author = {Amir Algom},
journal= {arXiv preprint arXiv:2504.18192},
year = {2025}
}
Comments
19 pages. Submitted to the proceedings of Fractal Geometry and Stochastics VII