@article{Xiaoqing2024, 
author = {Zhao Xiaoqing and Yi Yuan},
title = {Square-free numbers in the intersection of Lehmer set and Piatetski-Shapiro sequence},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {12},
pages = {33591-33609},
keywords = {Lehmer set, Piatetski-Shapiro sequence, square-free numbers, estimate methods of exponential sum, asymptotic properties},
url = {https://www.sciopen.com/article/10.3934/math.20241603},
doi = {10.3934/math.20241603},
abstract = {Let  q be a sufficiently large odd integer, and let  c∈(1,43). 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.}
}