The Dirichlet series of the arithmetic derivative

Es-said En-naoui

The Dirichlet series of the arithmetic derivative

General Mathematics 2023-05-17 v1

Authors: Es-said En-naoui

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: $\sum \limits_{n\geq 1} \frac{f(n)\delta(n)}{n^s}$ where $f$ is a classical arithmetic function.

Keywords

dirichlet series arithmetic derivative l-additive function von mangoldt function arithmetic function

Cite

@article{arxiv.2305.09445,
  title  = {The Dirichlet series of the arithmetic derivative},
  author = {Es-said En-naoui},
  journal= {arXiv preprint arXiv:2305.09445},
  year   = {2023}
}

Comments

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

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