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arXiv · 1908.01198

Mean value theorems for a class of density-like arithmetic functions

Lucas Reis
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Abstract

This paper provides a mean value theorem for arithmetic functions $f$ defined by $$f(n)=\prod_{d|n}g(d),$$ where $g$ is an arithmetic function taking values in $(0, 1]$ and satisfying some generic conditions. As an application of our main result, we prove that the density $\mu_q(n)$ (resp. $\rho_q(n)$) of normal (resp. primitive) elements in the finite field extension $\mathbb{F}_{q^n}$ of $\mathbb{F}_q$ are arithmetic functions of (non zero) mean values.

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Lucas Reis. 2019-08-03. Mean value theorems for a class of density-like arithmetic functions. https://arxiv.org/abs/1908.01198

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