THE FINAL SDSS HIGH-REDSHIFT QUASAR SAMPLE of 52 QUASARS at z > 5.7

We present the discovery of nine quasars at z ∼ 6 identified in the Sloan Digital Sky Survey (SDSS) imaging data. This completes our survey of z ∼ 6 quasars in the SDSS footprint. Our final sample consists of 52 quasars at 5.7 < z ≤ 6.4, including 29 quasars with z_AB ≤ 20 mag selected from 11,240 deg2 of the SDSS single-epoch imaging survey (the main survey), 10 quasars with 20 ≤ z_AB ≤ 20.5 selected from 4223 deg2 of the SDSS overlap regions (regions with two or more imaging scans), and 13 quasars down to z_AB ≈ 22 mag from the 277 deg² in Stripe 82. They span a wide luminosity range of -29.0 ≤ M₁₄₅₀ ≤ -24.5. This well-defined sample is used to derive the quasar luminosity function (QLF) at z ∼ 6. After combining our SDSS sample with two faint (M₁₄₅₀ ≥ -23 mag) quasars from the literature, we obtain the parameters for a double power-law fit to the QLF. The bright-end slope β of the QLF is well constrained to be β = -2.8 ± 0.2. Due to the small number of lowluminosity quasars, the faint-end slope α and the characteristic magnitude M^∗ ₁₄₅₀ are less well constrained, with =α= -1.90 ^+0.58 _-0.44 and M∗ = -25.2^+1.2 _-3.8mag. The spatial density of luminous quasars, parametrized as p(M₁₄₅₀<-26, z) = p(=6) 10^k(z-6), drops rapidly from z ∼ 5 to 6, with k = -0.72 ± 0.11. Based on our fitted QLF and assuming an intergalactic medium (IGM) clumping factor of C=3, we find that the observed quasar population cannot provide enough photons to ionize the z ∼ 6 IGM at ∼90% confidence. Quasars may still provide a significant fraction of the required photons, although much larger samples of faint quasars are needed for more stringent constraints on the quasar contribution to reionization.