The Luminosity Function of Quasars at Redshifts Greater than Four.

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We present results from two multicolor surveys for quasars at z > 4, one utilizing a widefield photographic technique aimed at detecting bright quasars, and a second survey for faint quasars using CCD imaging. We also conducted a CCD survey aimed at recovering z > 4 quasars previously found in a photographic survey by Irwin, McMahon, & Hazard, but not fully documented in the literature. We report spectra, redshifts, finding charts, magnitudes and coordinates for ten such quasars. The bright quasar survey utilizes the digitized Second Palomar Sky Survey. The plates are taken in the photographic JFN bands and calibrated to Gunn-Thuan gri, making these data suitable for a multicolor search for quasars at 4.0 _sp{~} < z _sp{~} < 4.8. Here we describe the search techniques and report the discovery of ten quasars. We have covered an effective area of 681 square degrees with 16.5m <=q r <=q 19.6m. Adopted selection criteria were applied objectively to the data sets, allowing the survey completeness to be estimated through Monte Carlo simulations, and quasar space densities at high redshift to be calculated. At our median redshift of z = 4.35, we find that quasar space densities are down by a factor of 7 from z = 2.0, and we see no evidence for luminosity dependent density evolution from z = 2 to z = 4. The original motivation for the faint CCD survey was to detect quasar clustering at high-redshift in order to constrain theories of structure formation at early epochs. Therefore, the majority of data reported are centered on fields containing known z > 4 quasars and a few are centered on blank control fields. We have selected a complete, rigorously defined sample of 39 quasar candidates from an area of 0.69 square degrees. Seven have been examined spectroscopically, confirming none as high-redshift quasars. However, we have surveyed enough area to constrain the z > 4 quasar luminosity function at M_ {B} < -{24.0}^{m }. We discuss future prospects for detecting quasar clustering at high-redshift using these techniques.

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