We consider eigenvalue sums of Schrödinger operators -+V on L^2 (^d) with complex radial potentials V L^q (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 (z₉) accumulate to a point in (0, ), then (Imz₉) 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.
Cuenin et al. (Mon,) studied this question.