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On the proximity of multiplicative functions to the number of distinct prime factors function

In: Mathematica Slovaca, vol. 68, no. 3
Jean-Marie De Koninck - Nicolas Doyon - François Laniel
Detaily:
Rok, strany: 2018, 513 - 526
Kľúčové slová:
additive functions, multiplicative functions, number of distinct prime factors of an integer
O článku:
Given an additive function $f$ and a multiplicative function $g$, let $E(f,g;x)=\#\{n≤ x: f(n)=g(n)\}$. We study the size of $E(ω,g;x)$ and $E(Ω,g;x)$, where $ω(n)$ stands for the number of distinct prime factors of $n$ and $Ω(n)$ stands for the number of prime factors of $n$ counting multiplicity. In particular, we show that $E(ω,g;x)$ and $E(Ω,g;x)$ are $O(\frac{x}{\sqrt{ log log x}})$ for any integer valued multiplicative function $g$. This improves an earlier result of De Koninck, Doyon and Letendre.
Ako citovať:
ISO 690:
De Koninck, J., Doyon, N., Laniel, F. 2018. On the proximity of multiplicative functions to the number of distinct prime factors function. In Mathematica Slovaca, vol. 68, no.3, pp. 513-526. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0121

APA:
De Koninck, J., Doyon, N., Laniel, F. (2018). On the proximity of multiplicative functions to the number of distinct prime factors function. Mathematica Slovaca, 68(3), 513-526. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0121
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