Estimates for multiplicative functions, II.

Abstract. In this paper we consider multiplicative functions \(f\) and \(g\), \(|f|\leq g\), as in Part I, and prove \(\sum\limits_{n\leq x}f(n)=\{1+o(1)\} x^{ia}(1+ia)^{-1}A_{x}\sum\limits_{n\leq x}g(n)\) if the series \(\sum\limits_{p}(g(p)-Ref(p)p^{-ia})p^{-1}\) converges for some \(a\in\mathbb R\).