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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.08448 |
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| _version_ | 1866929204395769856 |
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| author | Chan, Tsz Ho |
| author_facet | Chan, Tsz Ho |
| contents | Let $s_1, s_2, s_3, \cdots$ be the set of squarefree numbers in ascending order. In this paper, we prove that the following asymptotic on moments of gaps between squarefree numbers \[ \sum_{s_{k+1} \le x} (s_{k+1} - s_k)^γ\sim B(γ) x \; \; \mbox{ with some constant} \; \; B(γ) > 0 \] is true for $0 \le γ< 3.75$. This improves the previous best range $0 \le γ< 3.6875$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_08448 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On moments of gaps between consecutive squarefree numbers Chan, Tsz Ho Number Theory 11N25 Let $s_1, s_2, s_3, \cdots$ be the set of squarefree numbers in ascending order. In this paper, we prove that the following asymptotic on moments of gaps between squarefree numbers \[ \sum_{s_{k+1} \le x} (s_{k+1} - s_k)^γ\sim B(γ) x \; \; \mbox{ with some constant} \; \; B(γ) > 0 \] is true for $0 \le γ< 3.75$. This improves the previous best range $0 \le γ< 3.6875$. |
| title | On moments of gaps between consecutive squarefree numbers |
| topic | Number Theory 11N25 |
| url | https://arxiv.org/abs/2310.08448 |