Semi-classical correspondence and exact results : the case of the spectra of homogeneous Schrödinger operators

Version française : Comptes Rendus de l'Académie des Sciences Série I, 293 (1981) pp.709-712The semi-classical WKB method is liable to yield exact results in full generality. Such results, in the case of the Schrödinger operator with a homogeneous potential $q^{2M}$, appear as a functional equation obeyed by the Fredholm determinant, or as arithmetical identities satisfied by the Zeta function of the spectrum