Singularities of the Magnetic Spectral Shift Function for Potentials of Variable Sign

We consider the 3D-Schr & ouml;dinger operator Ho with constant magnetic field B of scalar intensity b > 0 and its perturbations H = H-o + V by a potential V of not necessarily fixed sign. Then we study the singularities at the Landau levels of the Kre & iuml;n spectral shift functions (sic)(-; H. Ho) for the pair (H, H-o). We consider power-like decaying potentials and cylindrically supported potentials (with axis B).