Square-free numbers in the intersection of Lehmer set and Piatetski-Shapiro sequence
Let $ q $ be a sufficiently large odd integer, and let $ c \in\left(1, \frac{4}{3}\right) $. We denote $ R(c; q) $ as the count of square-free numbers in the intersection of the Lehmer set and the Piatetski-Shapiro sequence. By employing additive character properties to transform congruence equation...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-11-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241603 |
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| Summary: | Let $ q $ be a sufficiently large odd integer, and let $ c \in\left(1, \frac{4}{3}\right) $. We denote $ R(c; q) $ as the count of square-free numbers in the intersection of the Lehmer set and the Piatetski-Shapiro sequence. By employing additive character properties to transform congruence equations and applying Kloosterman sums and methods of exponential sums, we derive a sharp asymptotic formula as $ q $ approaches infinity, which is significant for understanding the distribution properties of the Lehmer problem. |
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| ISSN: | 2473-6988 |