Taiwanese Journal of Mathematics

Power-free Values of Strongly $Q$-additive Functions

Karam Aloui, Mohamed Mkaouar, and Walid Wannes

Full-text: Open access

Abstract

Let $f$ be a strongly $q$-additive function with integer values. Given an integer $k \geq 2$, we try to estimate the number of positive integers $n \leq N$ (resp. primes $p \leq N$) for which $f(n)$ is $k$-free (resp. $f(p)$ is $k$-free).

Article information

Source
Taiwanese J. Math., Volume 23, Number 4 (2019), 777-798.

Dates
Received: 10 June 2018
Revised: 30 November 2018
Accepted: 16 December 2018
First available in Project Euclid: 18 July 2019

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1563436868

Digital Object Identifier
doi:10.11650/tjm/181208

Mathematical Reviews number (MathSciNet)
MR3982061

Zentralblatt MATH identifier
07088947

Subjects
Primary: 11A63: Radix representation; digital problems {For metric results, see 11K16} 11L03: Trigonometric and exponential sums, general 11N05: Distribution of primes 11N69: Distribution of integers in special residue classes

Keywords
$k$-free numbers strongly $q$-additive function exponential sums prime numbers

Citation

Aloui, Karam; Mkaouar, Mohamed; Wannes, Walid. Power-free Values of Strongly $Q$-additive Functions. Taiwanese J. Math. 23 (2019), no. 4, 777--798. doi:10.11650/tjm/181208. https://projecteuclid.org/euclid.twjm/1563436868


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