We investigate the high-redshift quasar luminosity function (QLF) down to an apparent magnitude of I AB = 25 in the Cosmic Evolution Survey (COSMOS). Careful analysis of the extensive COSMOS photometry and imaging data allows us to identify and remove stellar and low-redshift contaminants, enabling a selection that is nearly complete for type-1 quasars at the redshifts of interest. We find 155 likely quasars at z 3.1, 39 of which have prior spectroscopic confirmation. We present our sample in detail and use these confirmed and likely quasars to compute the rest-frame UV QLF in the redshift bins 3.1 z 3.5 and 3.5 z 5. The space density of faint quasars decreases by roughly a factor of four from z ~ 3.2 to z ~ 4, with faint-end slopes of β ~ –1.7 at both redshifts. The decline in space density of faint optical quasars at z 3 is similar to what has been found for more luminous optical and X-ray quasars. We compare the rest-frame UV luminosity functions found here with the X-ray luminosity function at z 3, and find that they evolve similarly between z ~ 3.2 and z ~ 4; however, the different normalizations imply that roughly 75% of X-ray bright active galactic nuclei (AGNs) at z ~ 3-4 are optically obscured. This fraction is higher than found at lower redshift and may imply that the obscured, type-2 fraction continues to increase with redshift at least to z ~ 4. Finally, the implications of the results derived here for the contribution of quasars to cosmic reionization are discussed.
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