On convoluted sums

Abstract. Given a complex valued multiplicative function \(f\) such that \(|f(n)|=1\) for each \(n\in {\mathbb N}\), let \(h_f(n) := \sum_{\nu =1}^{n-1} f(\nu) f(n-\nu)\). We investigate under which conditions we have \(h_f(n)=o(n)\) for almost all positive integers \(n\) as \(n\to \infty\).