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.