# Mathematical Communications,Vol. 25 No. 1, 2020.

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Asymptotics of partial sums of the Dirichlet series of the arithmetic derivative

Pentti Haukkanen
Jorma K. Merikoski
Timo Tossavainen

 Puni tekst: engleski, pdf (96 KB) str. 107-115 preuzimanja: 62* citiraj APA 6th EditionHaukkanen, P., Merikoski, J.K. i Tossavainen, T. (2020). Asymptotics of partial sums of the Dirichlet series of the arithmetic derivative. Mathematical Communications, 25 (1), 107-115. Preuzeto s https://hrcak.srce.hr/235544 MLA 8th EditionHaukkanen, Pentti, et al. "Asymptotics of partial sums of the Dirichlet series of the arithmetic derivative." Mathematical Communications, vol. 25, br. 1, 2020, str. 107-115. https://hrcak.srce.hr/235544. Citirano 12.04.2021. Chicago 17th EditionHaukkanen, Pentti, Jorma K. Merikoski i Timo Tossavainen. "Asymptotics of partial sums of the Dirichlet series of the arithmetic derivative." Mathematical Communications 25, br. 1 (2020): 107-115. https://hrcak.srce.hr/235544 HarvardHaukkanen, P., Merikoski, J.K., i Tossavainen, T. (2020). 'Asymptotics of partial sums of the Dirichlet series of the arithmetic derivative', Mathematical Communications, 25(1), str. 107-115. Preuzeto s: https://hrcak.srce.hr/235544 (Datum pristupa: 12.04.2021.) VancouverHaukkanen P, Merikoski JK, Tossavainen T. Asymptotics of partial sums of the Dirichlet series of the arithmetic derivative. Mathematical Communications [Internet]. 2020 [pristupljeno 12.04.2021.];25(1):107-115. Dostupno na: https://hrcak.srce.hr/235544 IEEEP. Haukkanen, J.K. Merikoski i T. Tossavainen, "Asymptotics of partial sums of the Dirichlet series of the arithmetic derivative", Mathematical Communications, vol.25, br. 1, str. 107-115, 2020. [Online]. Dostupno na: https://hrcak.srce.hr/235544. [Citirano: 12.04.2021.]

Sažetak
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.

Ključne riječi
Abscissa of convergence; arithmetic derivative; Dirichlet series

Hrčak ID: 235544

Posjeta: 136 *