Spectral density of the QCD Dirac operator near zero virtuality

We investigate the spectral properties of a random matrix model which in the large N limit embodies the essentials of the QCD partition function at low energy. The exact spectral density and its pair correlation function are derived for an arbitrary number of flavors and zero topological charge. Their microscopic limits provide the master formulae for sum rules for the inverse powers of the eigenvalues of the QCD Dirac operator, as recently discussed by Leutwyler and Smilga.