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 Three .
The sample extends from i = 15 to i = 19.1 at z \lesssim 3 and to i = 20.2 for z \gtrsim 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 where 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 ) \propto L ^ { \beta } ) .
Above z = 2.4 the slope flattens with redshift to \beta \gtrsim - 2.37 at z = 5 .
This slope change , which is significant at the \gtrsim 5 -sigma level , must be accounted for in models of the evolution of accretion onto supermassive black holes .