Uniform distribution of α n modulo one for a family of integer sequences
Abstract
We show that the sequence (α n)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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