The Dirichlet series of the arithmetic derivative

Abstract

The main object of this paper is to give the generalized von mangoldt function using the L-additive function which can help us to make it possible to calculate The Dirichlet series of the arithmetic derivative $\delta$ and Dirichlet series defined by: $$\sum _{n\ge 1}\frac{f(n)\delta (n)}{n^s}$$ where $f$ is a classical arithmetic function.

arXiv comment12. arXiv admin note: substantial text overlap with arXiv:2301.09677; substantial text overlap with arXiv:1803.06849 by other authors