Square-free numbers in the intersection of Lehmer set and Piatetski-Shapiro sequence

• Published in: AIMS mathematics Vol. 9; no. 12; pp. 33591 - 33609
• Main Authors: Xiaoqing, Zhao, Yuan, Yi
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2024
• Subjects: asymptotic properties; estimate methods of exponential sum; lehmer set; piatetski-shapiro sequence; square-free numbers

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...