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

We establish a smoothed asymptotic formula for the third moment of quadratic Dirichlet 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 x3/4. The error term in the asymptotic formula is on the order of O(x2/3+δ) for every δ > 0.