The Sloan Digital Sky Survey Quasar Survey: Quasar Luminosity Function from Data Release 3

We determine the number counts and z=0-5 luminosity function for a well-defined, homogeneous sample of quasars from the Sloan Digital Sky Survey (SDSS). We conservatively define the most uniform statistical sample possible, consisting of 15, 343 quasars within an effective area of 1622 deg² that was derived from a parent sample of 46, 420 spectroscopically confirmed broad-line quasars in the 5282 deg² of imaging data from SDSS Data Release Three. The sample extends from i=15 to i=19. 1 at z3. The number counts and luminosity function agree well with the results of the 2dF QSO Survey, but the SDSS data probe to much higher redshifts than does the 2dF sample. The number density of luminous quasars peaks between redshifts 2 and 3, although uncertainties in the selection function in this range do not allow us to determine the peak redshift more precisely. Our best fit model has a flatter bright end slope at high redshift than at low redshift. For z5-sigma level, must be accounted for in models of the evolution of accretion onto supermassive black holes.