Extrapolating the mean-values of multiplicative functions

Abstract

It is shown that certain commonly occurring conditions may be factored out of sums of multiplicative arithmetic functions.

A function is arithmetic if it is defined on the positive integers. Those complex-valued arithmetic functions g which satisfy the relation g(ab) = g(a)g(b) for all coprime pairs of positive integers a, b are here called multiplicative. In this paper g will be a multiplicative function which satisfies |g(n)| ≤ 1 for all positive integers n.