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 deg(2) that was derived from a parent sample of 46,420 spectroscopically confirmed broad-line quasars in the 5282 deg(2) of imaging data from SDSS Data Release 3. The sample extends from 15 to 19.1 at z less than or similar to 3 and to 20.2 for z greater than or similar to 3. The number counts and luminosity function agree well with the results of the Two Degree Field QSO Redshift Survey (2QZ) at redshifts and luminosities at which the SDSS and 2QZ quasar samples overlap, but the SDSS data probe to much higher redshifts than does the 2QZ 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 z < 2.4 the data are best fit by a redshift-independent slope of beta = -3.1 [Phi(L)alpha L-beta]. Above z=2.4 the slope flattens with redshift to beta greater than or similar to -2.37 at z=5. This slope change, which is significant at the greater than or similar to 5 sigma level, must be accounted for in models of the evolution of accretion onto supermassive black holes.