The QSO evolution derived from the HBQS and other complete QSO surveys

An Homogeneous Bright QSO Survey (HBQS) has been carried out in the framework of an ESO Key Programme. 327 QSOs (with M-B< - 23 and 0.3<z<2.2) have been selected over an area of 555 deg(2) in the magnitude range 15<B<18.75. For magnitudes brighter than B=16.4 the QSO surface density turns out to be a factor 2.2 higher than what measured by the PG survey, corresponding to a surface density of 0.013(-.005)(+.007) deg(-2). If the data from the Edinburgh QSO Survey are included, an overdensity of a factor 2.7 is observed, corresponding to a surface density of 0.016+/-0.005 deg(-2). In order to derive the QSO optical luminosity function we used Monte Carlo simulations that take into account the selection criteria, photometric errors, and QSO spectral slope distribution. We have combined our data with the Edinburgh QSO Survey, the Large Bright QSO Survey, Durham/AAT survey, ESO/AAT faint survey and the (ZM)B-2 survey. The luminosity function can be represented with a Pure Luminosity Evolution, L(z) proportional to (1 + z)(k), of a two power-law both for q(0)=0.5 and q(0)=0.1. For q(0)=0.5 the k evolution parameter is k=3.26+/-0.07, slower than the previous Boyle's (1992) estimate k=3.45. A flatter slope beta=-3.72+/-0.13 of the bright part of the luminosity function is also required. If a spread in the QSO spectral slope of sigma(gamma)=0.3 and 0.5 is taken into account, the k parameter drops to 3.2 and 3.0, respectively. The observed overdensity of bright QSOs is concentrated at redshifts lower than 0.6. It results that in the range 0.3<z<0.6 the luminosity function is flatter than observed at higher redshifts. In this redshift, range for M-B< - 25, 32 QSOs are observed instead of 19 expected from our best-fit PLE model. This feature requires a luminosity dependent luminosity evolution in order to adequately represent the data in the whole 0.3<z