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Uniform Distribution Theory
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Journal

Uniform Distribution Theory (UDT)


Volume & Issue

UDT. Volume 18. Issue 2


Published on

December, 2023


Pages

19-30


DOI

https://doi.org/10.2478/udt-2023-0011

Article

Uniform Distribution of αn Modulo One for A family of Integer Sequences


Authors

Andreas Weingartner


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.


Citation

Weingartner, A. (2023). Uniform Distribution of αn Modulo One for A family of Integer Sequences. Uniform distribution theory, 18(2), 19-30. https://doi.org/10.2478/udt-2023-0011