Ideal counting function in cubic fields

For a cubic algebraic extension K of ?, the behavior of the ideal counting function is considered in this paper. More precisely, let a _K (n) be the number of integral ideals of the field K with norm n, we prove an asymptotic formula for the sum \(\sum\nolimits_{n_1^2 + n_2^2 \leqslant x} {a_K \left( {n_1^2 + n_2^2 } \right)} \).