Uniform Distribution of αn Modulo One for A family of Integer Sequences
Abstract
We show that the sequence (αn)n∈ℬ is uniformly distributed modulo 1, for every irrational α, provided ℬ belongs to a certain family of integer sequences, which includes the prime, almost prime, squarefree, practical, densely divisible and lexicographical numbers. We also give an estimate for the discrepancy if α has finite irrationality measure.
Language: English
Page range: 19 - 30
Submitted on: Mar 28, 2023
Accepted on: Jun 30, 2023
Published on: Feb 24, 2025
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year
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© 2025 Andreas Weingartner, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.