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

2019/08/03 by Reis, Lucas
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1908.01198

Abstract

This paper provides a mean value theorem for arithmetic functions f defined by f(n)=∏_d|ng(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 μ_q(n) (resp. ρ_q(n)) of normal (resp. primitive) elements in the finite field extension \mathbbF_qⁿ of \mathbbF_q are arithmetic functions of (non zero) mean values.

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