A.A. Abramov, A. Aslanyan and E.B. Davies Bounds on complex eigenvalues and resonances (528K, Postscript) ABSTRACT. We obtain bounds on the complex eigenvalues of non-self-adjoint Schr\"odinger operators with complex potentials, and also on the complex resonances of self-adjoint Schr\"odinger operators. Our bounds are compared with numerical results, and are seen to provide useful information.