THE FINAL SDSS HIGH-REDSHIFT QUASAR SAMPLE OF 52 QUASARS AT z > 5.7.

We present the discovery of nine quasars at identified in the Sloan Digital Sky Survey (SDSS) imaging data. This completes our survey of quasars in the SDSS footprint. Our final sample consists of 52 quasars at , including 29 quasars with mag selected from 11,240 deg2 of the SDSS single-epoch imaging survey (the main survey), 10 quasars with selected from 4223 deg2 of the SDSS overlap regions (regions with two or more imaging scans), and 13 quasars down to mag from the 277 deg2 in Stripe 82. They span a wide luminosity range of . This well-defined sample is used to derive the quasar luminosity function (QLF) at . After combining our SDSS sample with two faint ( 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 . Due to the small number of low-luminosity quasars, the faint-end slope α and the characteristic magnitude are less well constrained, with and mag. The spatial density of luminous quasars, parametrized as , drops rapidly from to 6, with . 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 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. [ABSTRACT FROM AUTHOR]