On a criterion of uniform distribution

2024/08/13 by Karagulyan, Grigori, Petrosyan, Iren
#11J71 #11K06 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.07061

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 Δ²x_n→ 0, n²Δ²x_n→ ∞ . 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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