Suppose K is a number field and \(a_K(m)\) is the number of integral ideals of norm equal to m in K, then for any integer l, we asymptotically evaluate the sum \(\begin{aligned} \sum _{m\leqslant T} a_K^l(m) \end{aligned}\) as \(T\rightarrow \infty \) . We also consider the moments of the corresponding Dedekind zeta-function. We prove lower bounds of expected order of magnitude and slightly improve the known upper bound for the second moment in the non-Galois case.
