X-ray QSO evolution from a very deep ROSAT survey

In the deepest optically identified X-ray survey yet performed, we have identified 32 X-ray selected QSOs to a flux limit of 2x10^{-15} erg cm^{-2} s^{-1} (0.5-2 keV). The survey, performed with the ROSAT PSPC, has 89% spectroscopic completeness. The QSO log(N)-log(S) relation is found to have a break to a flat slope at faint fluxes. The surface density of QSOs at the survey limit is 230+/-40 per square degree, the largest so far of any QSO survey. We have used this survey to measure the QSO X-ray luminosity function at low luminosities (Lx<10^{44.5} erg s^{-1}) and high redshifts (1<z