Average value of some certain types of arithmetic functions with Piatetski-Shapiro sequences
- 4 August 2022
- journal article
- research article
- Published by Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences) in Notes on Number Theory and Discrete Mathematics
- Vol. 28 (3), 500-506
- https://doi.org/10.7546/nntdm.2022.28.3.500-506
Abstract
In this paper, we study asymptotic behaviour of the sum Sigma(n <= N) f (left perpendicular n(c) right perpendicular), where f(n) = Sigma(d2 vertical bar n) g(d) under three different types of assumptions on g and 1 < c < 2.Keywords
This publication has 13 references indexed in Scilit:
- Square-full numbers in Piatetski–Shapiro sequencesAnnales mathématiques du Québec, 2020
- Note on a paper by Bordellès, Dai, Heyman, Pan and ShparlinskiPeriodica Mathematica Hungarica, 2019
- On a sum involving the Euler functionJournal of Number Theory, 2019
- On a sum involving the Euler functionJournal of Number Theory, 2019
- Distribution of cube-free numbers with form [nc]Frontiers of Mathematics in China, 2017
- Friable values of Piatetski-Shapiro sequencesProceedings of the American Mathematical Society, 2017
- Squares in Piatetski-Shapiro sequencesActa Arithmetica, 2017
- Almost primes of the formIndagationes Mathematicae, 2016
- CHARACTER SUMS WITH PIATETSKI-SHAPIRO SEQUENCESThe Quarterly Journal of Mathematics, 2015
- Piatetski-Shapiro sequencesActa Arithmetica, 2013