%0 Journal Article
%T Asymptotics of partial sums of the Dirichlet series of the arithmetic derivative
%A Haukkanen
%A Pentti
%A Merikoski
%A Jorma K.
%A Tossavainen
%A Timo
%J -
%D 2020
%X Sa£żetak Let $p\in\mathbb P$ and $s\in\mathbb R$, and suppose that$\emptyset\ne P\subset\mathbb P$ is finite.Given $n\in\mathbb Z_+$, let $n'$, $n'_p$, and $n'_P$ denote respectively its arithmetic derivative, arithmetic partial derivative with respect to~$p$,and arithmetic subderivative with respect to~$P$. We study the asymptotics of $$\sum_{1\le n\le x}\frac{n'}{n^s},\,\sum_{1\le n\le x}\frac{n'_p}{n^s},\quad{\rm and}\,\,\sum_{1\le n\le x}\frac{n'_P}{n^s}.$$ We also show that the abscissa of convergence of the corresponding Dirichlet series equals~two
%K Abscissa of convergence
%K arithmetic derivative
%K Dirichlet series
%U https://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=342235