Relatively prime pairs in the Piatetski-Shapiro sequences

Yuta Suzuki

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arXiv · 2403.10866

Relatively prime pairs in the Piatetski-Shapiro sequences

Yuta Suzuki

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Abstract

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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Yuta Suzuki. 2024-03-16. Relatively prime pairs in the Piatetski-Shapiro sequences. https://arxiv.org/abs/2403.10866

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