@article{Fan2025, 
author = {Haihong Fan},
title = {A class of small multiplicative functions in Piatetski-Shapiro sequences},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {12},
pages = {28514-28523},
keywords = {Piatetski-Shapiro sequences, multiplicative function, small value, exponential sum, distribution of primes},
url = {https://www.sciopen.com/article/10.3934/math.20251255},
doi = {10.3934/math.20251255},
abstract = {For any real number    x  ,  [  x  ] denotes the integer part of    x.              F              1       denotes a class of multiplicative functions that are small in a numerical sense. In this paper, we study the distribution of the functions from              F              1       in Piatetski-Shapiro sequences. In particular, we prove that for    1  <  c  <      4    3    ,         ∑                                        f            ∈                                          F                                            1                                                          n            ≤            x                                f  (  [      n          c        ]  )  =      ∫          1                      x                  c                      γ      u          γ      −      1        d      (                  ∑                  1          ≤          n          ≤          u                    f      (      n      )        )    +  O  (      x          1      −      ε        )  ,where    γ  =      1    c   and    [      n          c        ] is the Piatetski-Shapiro sequence.}
}