Asymptotics on the Number of Scattering Poles for Degenerate Perturbations of the Laplacian

For a class of compactly supported hypoelliptic perturbations of the Laplacian inRn,n⩾3 odd, we prove that an asymptotic on the number of the eigenvalues of the corresponding reference operator implies a similar asymptotic for the number of the scattering poles.