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We present the discovery of five quasars at z~6 selected from 260 deg^2 ofthe Sloan Digital Sky Survey (SDSS) southern survey, a deep imaging surveyobtained by repeatedly scanning a stripe along the Celestial Equator. The fivequasars with 20<z_{AB}<21 are 1-2 magnitudes fainter than the luminous z~6quasars discovered in the SDSS main survey. One of them was independentlydiscovered by the UKIRT Infrared Deep Sky Survey. These quasars, combined withanother z~6 quasar known in this region, make a complete flux- limited quasarsample at z_{AB}<21. The sample spans the redshift range 5.85<z<6.12 and theluminosity range -26.5<M_{1450}<-25.4 (H_0=70 km s^{-1} Mpc^{-1},Omega_{m}=0.3, and Omega_{Lambda}=0.7). We use the 1/V_{a} method to determinethat the comoving quasar spatial density at <z>=6.0 and <M_{1450}>=-25.8 is(5.0+/-2.1) x 10^{-9} Mpc^{-3} mag^{-1}. We model the bright-end quasarluminosity function (QLF) at z~6 as a power law Phi(L_{1450}) \proptoL_{1450}^{beta}. The slope beta calculated from a combination of our sample andthe luminous SDSS quasar sample is -3.1+/-0.4, significantly steeper than theslope of the QLF at z~4. Based on the derived QLF, we find that the quasar/AGNpopulation cannot provide enough photons to ionize the intergalactic medium(IGM) at z~6 unless the IGM is very homogeneous and the luminosity (L*_{1450})at which the QLF power law breaks is very low.

A Survey of z~6 Quasars in the SDSS Deep Stripe: I. a Flux-Limited Sample at z_{AB}<21