Mean values related to the Dedekind zeta-function

Let K/& Qopf; be a nonnormal cubic extension which is given by an irreducible polynomial g(x) = x(3) + ax(2) + bx + c. Denote by zeta k(s) the Dedekind zeta-function of the field K and a(K)(n) the number of integral ideals in K with norm n. In this note, by the higher integral mean values and subconvexity bound of automorphic L-functions, the second and third moment of aK(n) is considered, i.e. & sum;(n <= x)a(K)(2)(n)=xP1(logx)+O(x(5/7+epsilon)),& sum;(n <= x)a(K)(3)(n)=xP(4)(logx)+O(X321/356+epsilon), where P-1(t), P-4(t) are polynomials of degree 1, 4, respectively, epsilon > 0 is an arbitrarily small number.