On the Riesz means of -II

Let phi(n) denote the Euler-totient function. We study the error term of the general k-th Riesz mean of the arithmetical function n f( n) for any positive integer k >= 1, namely the error term E-k(x) where 1/k! Sigma(n <= x) n/phi(n) (1 - n/x)(k) = M-k(x) + E-k(x). The upper bound for vertical bar E-k(x)vertical bar established here thus improves the earlier known upper bounds for all integers k >= 1.