  We prove that the resonances of long range perturbations of the
(semiclassical) Laplacian are the zeroes of natural perturbation determinants.
We more precisely obtain factorizations of these determinants of the form $
\prod_{w = {\rm resonances}}(z-w) \exp (\varphi_p(z,h)) $ and give
semiclassical bounds on $ \partial_z \varphi_p $ as well as a representation of
Koplienko's regularized spectral shift function. Here the index $ p \geq 1 $
depends on the decay rate at infinity of the perturbation.
