The evolution rate of quasars at various redshifts
  The evolution of optically selected quasars is usually supposed to be well described by a single constant parameter, either k_L or k_D, depending whether we refer to luminosity or density evolution. In this paper we present a study of the variations of the evolution parameters with redshift, for different cosmological models, in order to probe the differential evolution with redshift. Two different quasar samples have been analyzed, the AAT Boyle's et al. and the LBQS catalogues. Basically, these samples are divided in redshift intervals and in each of them k_L and k_D are estimated by forcing that <V/Vmax>=0.5. The dependence with respect to the cosmological parameters is small. Both AAT and LBQS show roughly the same tendencies. LBQS, however, shows strong fluctuations, whose origin is not statistical but rather due to the selection criteria. A discussion on selection techniques, biases and binning effects explains the differences between these results. We finally conclude that the evolution parameter is almost constant in the redshift range 0.7 < z < 1.7, at least within 2 sigma, while it decreases slightly afterwards. Results depend on the binning chosen (but not in a very significant way). The method has been tested with Monte-Carlo simulated catalogues in order to give a better understanding of the results coming from the real catalogues. A correlation between k_L (k_D) and <V/Vmax> is also derived and is used for the calculation of the error bars on the evolution parameter. 
Evanthia Hatziminaoglou, Ludovic Van Waerbeke, Guy Mathez   (Observatoire Midi-Pyrenees, Toulouse)