A survey of high -redshift quasars from the Sloan Digital Sky Survey

In this thesis, I carry out a survey for high-redshift quasars using Sloan Digital Sky Survey imaging data, and use this sample to study the evolution of high-redshift quasars.;I first develop a Monte-Carlo simulation of the distribution of quasars, stars and compact galaxies in SDSS color space, in order to study the evolution of quasar colors and to establish the algorithm to select quasars using SDSS data. The algorithm is applied to ∼400 deg2 of five-color imaging data taken during the SDSS commissioning phase to select high-redshift quasar candidates. In the thesis, I present the discovery of ∼70 quasars at z > 3.6 along the Celestial Equator. Thirty-nine of the quasars form a complete color-selected sample covering 182 deg2 of the Fall Equatorial Stripe at i' ≲ 20 over the redshift range 3.6 < z < 5.0. The efficiency of the quasar target selection is ∼70%, and the average survey completeness is ∼75%.;I develop statistical techniques for treating complicated selection functions, and derive the quasar luminosity function in both parametric and non-parametric forms, using the Fall Equatorial Stripe sample. Consistent with previous studies using smaller samples, the results show that the number density of luminous quasars declines rapidly towards high redshift. This trend continues to at least z ∼ 5, with the quasar density decreasing by a factor of ∼20 from z ∼ 3. The bright-end slope of the high-redshift quasar luminosity function is considerably shallower than that at low redshift, indicating that there is significant evolution in the shape of the quasar luminosity function as well.;A peculiar quasar at z = 4.62 without detectable emission lines is discovered in the survey. This quasar also lacks radio emission and optical polarization, indicating that it is not a simple counterpart of the low-redshift BL Lac population. It might represent a new class of AGN at high redshift.;I also present observations of a very luminous quasar at z = 5.80 found from the SDSS data. The lack of a Gunn-Peterson trough in its spectrum indicates that the universe is already highly ionized at z ∼ 5.8. The abundance and evolution of such quasars can provide sensitive tests of models of quasar and galaxy evolution.