The QSO evolution derived from the HBQS and other complete QSO surveys
  An ESO Key programme dedicated to an Homogeneous Bright QSO Survey (HBQS) has been completed. 327 QSOs (Mb<-23, 0.3<z<2.2) have been selected over 555 deg^2 with 15<B<18.75. For 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+/-.006 deg^{-2}. If the Edinburgh QSO Survey is included, an overdensity of a factor 2.5 is observed, corresponding to a density of 0.016+/-0.005 deg^{-2}. In order to derive the QSO optical luminosity function (LF) we used Monte Carlo simulations that take into account of the selection criteria, photometric errors and QSO spectral slope distribution. The LF can be represented with a Pure Luminosity Evolution (L(z)\propto(1+z)^k) of a two power law both for q_0=0.5 and q_0=0.1. For q_0=0.5 k=3.26, slower than the previous Boyle's (1992) estimations of k=3.45. A flatter slope beta=-3.72 of the bright part of the LF is also required. The observed overdensity of bright QSOs is concentrated at z<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 Mb<-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 satisfactorily represent the data in the whole 0.3<z<2.2 interval. 
Fabio La Franca (Dip. di Fisica, Univ. Roma TRE), and Stefano   Cristiani (Dip. di Astronomia, Univ. di Padova)