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arXiv · 2408.07061

On a criterion of uniform distribution

Grigori Karagulyan·Iren Petrosyan
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Abstract

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 $\Delta^2x_n\to 0,\quad n^2\Delta^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.

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Grigori Karagulyan, Iren Petrosyan. 2024-08-13. On a criterion of uniform distribution. https://arxiv.org/abs/2408.07061

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