@article{Shen2023, 
author = {Yukai Shen},
title = {kth powers in a generalization of Piatetski-Shapiro sequences},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {9},
pages = {22411-22418},
keywords = {kth power, Piatetski-Shapiro sequence, exponential sum, asymptotic formula},
url = {https://www.sciopen.com/article/10.3934/math.20231143},
doi = {10.3934/math.20231143},
abstract = {The article considers a generalization of Piatetski-Shapiro sequences in the sense of Beatty sequences. The sequence is defined by              (              ⌊                  α                      n            c                    +          β                ⌋            )              n      =      1              ∞      , where    α  ≥  1,    c  >  1, and    β are real numbers.The focus of the study is on solving equations of the form        ⌊          α              n        c            +      β        ⌋    =  s      m    k  , where    m and    n are positive integers,    1  ≤  n  ≤  N, and    s is an integer. Bounds for the solutions are obtained for different values of the exponent    k, and an average bound is derived over    k-free numbers    s in a given interval.}
}