Lower bounds for the counting function of resonances for a perturbation of a periodic Schrodinger operator by decreasing potential

We are interested here in the counting function of resonances N(h) for a perturbation of a periodic Schrodinger operator P-0 by decreasing potential W(hx) (h SE arrow 0). We obtain a lower bound for N(h) near some singularities of the density of states measure, associated to the unperturbed Hamiltonian P-0. (C) 2002 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.