Liminf-results for sums with Kronecker sequence
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866929733927698432 |
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| author | Chebotarenko, Artem |
| author_facet | Chebotarenko, Artem |
| contents | For irrational $θ$ and 1-periodic function $f$ we consider sums $\sum_0^{Q-1}f(kθ+φ)$ where $φ\in \mathbb R$. Sidorov proved that if $f$ is absolutely continuous function, then $\liminf_{Q \to \infty} |\sum_0^{Q-1}f(kθ+φ)| = 0$ for any irrational $θ$ and any $φ\in \mathbb R$. The article shows that this property is not a criterion of absolute continuity, and also obtains some other results concerning the liminf-properties of these sums. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19636 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Liminf-results for sums with Kronecker sequence Chebotarenko, Artem Number Theory For irrational $θ$ and 1-periodic function $f$ we consider sums $\sum_0^{Q-1}f(kθ+φ)$ where $φ\in \mathbb R$. Sidorov proved that if $f$ is absolutely continuous function, then $\liminf_{Q \to \infty} |\sum_0^{Q-1}f(kθ+φ)| = 0$ for any irrational $θ$ and any $φ\in \mathbb R$. The article shows that this property is not a criterion of absolute continuity, and also obtains some other results concerning the liminf-properties of these sums. |
| title | Liminf-results for sums with Kronecker sequence |
| topic | Number Theory |
| url | https://arxiv.org/abs/2502.19636 |