Extrapolating the mean-values of multiplicative functions

AbstractIt 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