On quantitative mean value estimations for multiplicative functions

Abstract. In this paper we use the convolution identity of Indlekofer to derive quantitative mean value estimations for a class of multiplicative functions \(f\) the values of which at primes satisfy \(|f(p)-\kappa|\leq \eta < \kappa\) where \(\kappa>1/2\). This generalizes earlier results by Halász and Elliott which are valid only for completely multiplicative functions and for the case \(\kappa=1\).