Singularities of the magnetic spectral shift function for potentials of variable sign

We consider the 3D-Schrödinger operator H_{0} with constant magnetic field B of scalar intensity b>0 , and its perturbations H= H_{0}+V by a potential V of not necessarily fixed sign. Then we study the singularities at the Landau levels of the Kreĭn spectral shift functions \xi(\cdot;H,H_{0}) for the pair (H,H_{0}) . We consider power-like decaying potentials and cylindrically supported potentials (with axis B ).