In a recent paper, J. Kaczorowski defined the generalized Euler totient function $\varphi(n, F)$ corresponding to a polynomial Euler product $F$. Let $E(x, F)$ denote the error term in the asymptotic formula of the summatory function of $\varphi(n, F).$ 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.
"On a generalization of the Euler totient function." Funct. Approx. Comment. Math. 65 (1) 119 - 139, September 2021. https://doi.org/10.7169/facm/1917