Year: 2025
Type: article
Abstract: We consider approximation properties of real points by uniformly distributed sequences. Under some assumptions on the approximation functions, we prove a Khintchine‐type 0‐1 dichotomy law. We establish a new connection between uniform distribution and the ubiquity property. Namely, we show that a bound on the discrepancy of the sequence implies the ubiquity property, which helps to obtain divergence results. We further obtain Hausdorff dimension results for weighted sets. The key tools in proving these results are the weighted ubiquitous systems and weighted mass transference principle introduced recently by Kleinbock and Wang, and Wang and Wu, respectively.
DOI: 10.1112/blms.70169
Authors: Gerardo González Robert, Mumtaz Hussain, Nikita Shulga, Benjamin Ward
Institutions: La Trobe University, University of York
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1291480630, G364613455
OpenAlex ID: W7104843354