The optical luminosity evolution function of quasars. I. A statistical evolution function that includes the large redshift range above redshift 2.2

We have redetermined the parameters in the Heisler-Ostriker quasar evolution formula so as to make it applicable to a larger redshift range. The form of the formula is appropriate because, physically, any variation in the mass of the central black hole and the accretion rate will cause a luminosity evolution while the birth of quasars will imply a luminosity-dependent density evolution. With our new parameters, we can 1) reproduce the quasar magnitude count down to magnitude 22.0, 2) reproduce the quasar redshift distribution in intervals of ΔZ = 0.1 and 3) substantially lessen the excess count for Z > 2 redicted by previous formulae.