Sommes courtes de certaines fonctions multiplicatives

Abstract

The purpose of this paper is to establish upper bounds for some short sums of a class of multiplicative functions over integers with certain restrictions on the number of prime factors. More precisely, we consider sums expressed in the form [Formula: see text]; or more generally [Formula: see text] where f is a positive multiplicative function, G is a polynomial with integer coefficients, and as usual, [Formula: see text] denotes the number of distinct prime factors of the integer m.