The ideal counting function in cubic fields

For a cubic algebraic extension $K$ of $mathbb{Q}$, the behavior of the ideal counting function is considered in this paper. Let $a_{K}(n)$ be the number of integral ideals of the field $K$ with norm $n$. An asymptotic formula is given for the sum $$ sumlimits_{n_{1}^2+n_{2}^2leq x}a_{K}(n_{1}^2+n_{2}^2). $$