High-Redshift Quasars Found in Sloan Digital Sky Survey Commissioning   Data IV: Luminosity Function from the Fall Equatorial Stripe Sampl
  This is the fourth paper in a series aimed at finding high-redshift quasars from five-color imaging data taken along the Celestial Equator by the SDSS. during its commissioning phase. In this paper, we use the color-selected sample of 39 luminous high-redshift quasars presented in Paper III to derive the evolution of the quasar luminosity function over the range of 3.6<z<5.0, and -27.5<M_1450<-25.5 (Omega=1, H_0=50 km s^-1 Mpc^-1). We use the selection function derived in Paper III to correct for sample incompleteness. The luminosity function is estimated using three different methods: (1) the 1/V_a estimator; (2) a maximum likelihood solution, assuming that the density of quasars depends exponentially on redshift and as a power law in luminosity and (3) Lynden-Bell's non-parametric C^- estimator. All three methods give consistent results. The luminous quasar density decreases by a factor of ~ 6 from z=3.5 to z=5.0, consistent with the decline seen from several previous optical surveys at z<4.5. The luminosity function follows psi(L) ~ L^{-2.5} for z~4 at the bright end, significantly flatter than the bright end luminosity function psi(L) \propto L^{-3.5} found in previous studies for z<3, suggesting that the shape of the quasar luminosity function evolves with redshift as well, and that the quasar evolution from z=2 to 5 cannot be described as pure luminosity evolution. Possible selection biases and the effect of dust extinction on the redshift evolution of the quasar density are also discussed. 
X. Fan, M. A. Strauss,, D. P. Schneider, J. E. Gunn, R. H. Lupton, R.   H. Becker, M. Davis, J. A. Newman, G. T. Richards, R...