On the third moment of L(tfrac{1}{2}, chi_d) II: the number field case

We establish a smoothed asymptotic formula for the third moment of quadratic {D}irichlet $L$-functions at the central value. In addition to the main term, which is known, we prove the existence of a secondary term of size $x^{\frac{3}{4}}$. The error term in the asymptotic formula is on the order of $O(x^{\frac{2}{3}+\delta})$ for every $\delta > 0.$