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 <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.
No takes yet. Share an insight, caveat, or question.
Yuta Suzuki (2024) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: