On a criterion of uniform distribution
We give an extension of a criterion of van der Corput on uniform distribution of sequences. Namely, we prove that a sequence $x_n$ is uniformly distributed modulo 1 if it is weakly monotonic and satisfies the conditions $Δ^2x_n\to 0,\quad n^2Δ^2x_n\to \infty $. Our proof is straightforward and uses a Diophantine approximation by rational numbers, while van der Corput's approach is based on some estimates of exponential sums.
math.CA↗