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

Weingartner, Andreas

doi:10.2478/udt-2023-0011

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.

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

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