Bounds for eigenvalue sums of Schrödinger operators with complex radial potentials

We consider eigenvalue sums of Schrödinger operators -Δ+V on L²(ᵈ) with complex radial potentials V∈ Lq(Rᵈ) , q<d . We prove quantitative bounds on the distribution of the eigenvalues in terms of the Lq norm of V . A consequence of our bounds is that, if the eigenvalues (zⱼ) accumulate to a point in (0,∞) , then (Imzⱼ) 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.