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 awell-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 deg^2 that wasderived from a parent sample of 46,420 spectroscopically confirmed broad-linequasars in the 5282 deg^2 of imaging data from SDSS Data Release Three. Thesample extends from i=15 to i=19.1 at z<3 and to i=20.2 for z>3. The numbercounts and luminosity function agree well with the results of the 2dF QSOSurvey, but the SDSS data probe to much higher redshifts than does the 2dFsample. The number density of luminous quasars peaks between redshifts 2 and 3,although uncertainties in the selection function in this range do not allow usto determine the peak redshift more precisely. Our best fit model has a flatterbright end slope at high redshift than at low redshift. For z<2.4 the data arebest fit by a redshift-independent slope of beta = -3.1 (Phi(L) propto L^beta).Above z=2.4 the slope flattens with redshift to beta=-2.37 at z=5. This slopechange, which is significant at a >5-sigma level, must be accounted for inmodels of the evolution of accretion onto supermassive black holes.Comment: 57 pages, 21 figures (9 color); minor changes to reflect the version accepted by AJ; higher resolution version available at ftp://ftp.astro.princeton.edu/gtr/dr3qlf/Feb1306