Bounds for eigenvalue sums of Schrödinger operators with complex radial potentials

We consider eigenvalue sums of Schrödinger operators -\Delta+V on L^{2}(\R^{d}) with complex radial potentials V\in L^{q}(\mathbb{R}^{d}) , q<d . We prove quantitative bounds on the distribution of the eigenvalues in terms of the L^{q} norm of V . A consequence of our bounds is that, if the eigenvalues (z_{j}) accumulate to a point in (0,\infty) , then (\operatorname{Im}z_{j}) is summable. The key technical tools are resolvent estimates in Schatten spaces. We show that these resolvent estimates follow from spectral measure estimates by an epsilon removal argument.