Average value of some certain types of arithmetic functions with Piatetski-Shapiro sequences

Suphawan Janphaisaeng, Teerapat Srichan and Pinthira Tangsupphathawat
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 3, Pages 500–506
DOI: 10.7546/nntdm.2022.28.3.500-506
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Authors and affiliations

Suphawan Janphaisaeng
Department of Mathematics, Faculty of Science, Naresuan University
Phitsanulok 65000, Thailand

Teerapat Srichan
Department of Mathematics, Faculty of Science, Kasetsart University
Bangkok 10900, Thailand

Pinthira Tangsupphathawat
Department of Mathematics, Faculty of Science and Technology, Phranakorn Rajabhat University
Bangkok 10220, Thailand

Abstract

In this paper, we study asymptotic behaviour of the sum \sum_{n\leq N}{f}\Big(\lfloor n^c \rfloor\Big), where f(n)=\sum_{d^2\mid n}g(d) under three different types of assumptions on g and 1<c<2.

Keywords

  • Arithmetic function, Piatetski-Shapiro sequences

2020 Mathematics Subject Classification

  • 11N37, 11N69

References

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Manuscript history

  • Received: 2 March 2022
  • Revised: 25 July 2022
  • Accepted: 2 August 2022
  • Online First: 4 August 2022

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Cite this paper

Janphaisaeng, S., Srichan, T., & Tangsupphathawat, P. (2022). Average value of some certain types of arithmetic functions with Piatetski-Shapiro sequences. Notes on Number Theory and Discrete Mathematics, 28(3), 500-506, DOI: 10.7546/nntdm.2022.28.3.500-506.

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