Relatively prime pairs in the Piatetski-Shapiro sequences
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 ingredient...
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Main Author | |
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Format | Journal Article |
Language | English |
Published |
16.03.2024
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Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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DOI: | 10.48550/arxiv.2403.10866 |