ON A GENERALIZATION OF THE EULER TOTIENT FUNCTION

摘要

In a recent paper, J. Kaczorowski defined the generalized Euler totient function phi(n, F) corresponding to a polynomial Euler product F. Let E(x, F) denote the error term in the asymptotic formula of the summatory function of phi(n, F). J. Kaczorowski proved that the mean square of E(x, F) has an asymptotic formula if F satisfies GRH. In this paper we shall prove a sharper asymptotic formula under GRH.