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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.07061 |
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| _version_ | 1866913467515011072 |
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| author | Karagulyan, Grigori Petrosyan, Iren |
| author_facet | Karagulyan, Grigori Petrosyan, Iren |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07061 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a criterion of uniform distribution Karagulyan, Grigori Petrosyan, Iren Classical Analysis and ODEs 11K06, 11J71 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. |
| title | On a criterion of uniform distribution |
| topic | Classical Analysis and ODEs 11K06, 11J71 |
| url | https://arxiv.org/abs/2408.07061 |