Let

Abstract. We consider the 3D Schrodinger operator H = H0 + V where H0 = (ir A)2 b, A is a magnetic potential generating a constant magnetic eld of strength b> 0, and V is a short-range electric potential which decays superexponentially with respect to the variable along the magnetic eld. We show that the resolvent of H admits a meromorphic extension from the upper half plane to an appropriate Riemann surface M, and dene the resonances of H as the poles of this meromorphic extension. We study their distribution near any xed Landau level 2bq, q 2 N. First, we obtain a sharp upper bound of the number of resonances in a vicinity of 2bq. Moreover, under appropriate hypotheses, we establish corresponding lower bounds which imply the existence of an in nite number of resonances, or the absence of resonances in certain sectors adjoining 2bq. Finally, we deduce a representation of the derivative of the spectral shift function (SSF) for the operator pair (H;H0) as a sum of a harmonic measure related to the resonances, and the imaginary part of a holomorphic function. This representation justies the Breit-Wigner approximation, implies