Relatively prime pairs in the Piatetski-Shapiro sequences
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913267220217856 |
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| author | Suzuki, Yuta |
| author_facet | Suzuki, Yuta |
| contents | In this paper, we prove an asymptotic formula for the number of relatively prime pairs in the Piatetski-Shapiro sequence of arbitrarily large order. This improves the result of Pimsert, Srichan and Tangsupphathawat (2023), the order of which was restricted to be $<\frac{3}{2}$. The key ingredients of the proof are a simple averaging trick and an extension of Deshouillers' result on the distribution of the Piatetski-Shapiro sequence in arithmetic progressions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10866 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relatively prime pairs in the Piatetski-Shapiro sequences Suzuki, Yuta Number Theory Primary: 11N25, Secondary: 11L03, 11L07 In this paper, we prove an asymptotic formula for the number of relatively prime pairs in the Piatetski-Shapiro sequence of arbitrarily large order. This improves the result of Pimsert, Srichan and Tangsupphathawat (2023), the order of which was restricted to be $<\frac{3}{2}$. The key ingredients of the proof are a simple averaging trick and an extension of Deshouillers' result on the distribution of the Piatetski-Shapiro sequence in arithmetic progressions. |
| title | Relatively prime pairs in the Piatetski-Shapiro sequences |
| topic | Number Theory Primary: 11N25, Secondary: 11L03, 11L07 |
| url | https://arxiv.org/abs/2403.10866 |