| Autor: |
Zhao Xiaoqing, Yi Yuan |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
|
| Zdroj: |
AIMS Mathematics, Vol 9, Iss 12, Pp 33591-33609 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.20241603?viewType=HTML |
| Popis: |
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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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