Mean values connected with the Dedekind zeta-function of a non-normal cubic field

After Landau's famous work, many authors contributed to some mean values connected with the Dedekind zeta-function. In this paper, we are interested in the integral power sums of the coefficients of the Dedekind zeta function of a non-normal cubic extension K-3/Q, i.e. S-l,S-K3(x) = Sigma(m <= x) M-l(m), where M(m) denotes the number of integral ideals of the field K-3 of norm m and l is an element of N. We improve the previous results for S-2,S-K3(x) and S-3,S-K3(x).