Hyperbolic summation for functions of the GCD and LCM of several integers

Abstract

Let k ≥ 2 be a fixed integer. We consider sums of type n1In particular, we deduce asymptotic formulas with remainder terms for the hyperbolic summations n1the GCD and LCM of the integers n 1 , . . . , n k , where f : N → C belongs to certain classes of functions. Some of our results generalize those obtained by the authors [5] for k = 2.