High-redshift QSOs in the SWIRE survey and the z similar to 3 QSO luminosity function

We use a simple optical/infrared (IR) photometric selection of high-redshift QSOs that identifies a Lyman break in the optical photometry and requires a red IR color to distinguish QSOs from common interlopers. The search yields 100 z similar to 3 ( U-dropout) QSO candidates with 19 < r ' < 22 over 11.7 deg(2) in the ELAIS-N1 (EN1) and ELAIS-N2 (EN2) fields of the Spitzer Wide-area Infrared Extragalactic (SWIRE) Legacy Survey. The z similar to 3 selection is reliable, with spectroscopic follow-up of 10 candidates confirming that they are all QSOs at 2.83 < z < 3.44. We find that our z similar to 4 (g '-dropout) sample suffers from both unreliability and incompleteness but present seven previously unidentified QSOs at 3.50 < z < 3.89. Detailed simulations show our z similar to 3 completeness to be similar to 80%-90% from 3.0 < z < 3.5, significantly better than the similar to 30%-80% completeness of the SDSS at these redshifts. The resulting luminosity function extends 2 mag fainter than SDSS and has a faint-end slope of beta = -1.42 +/- 0.15, consistent with values measured at lower redshift. Therefore, we see no evidence for evolution of the faint-end slope of the QSO luminosity function. Including the SDSS QSO sample, we have now directly measured the space density of QSOs responsible for similar to 70% of the QSO UV luminosity density at z similar to 3. We derive a maximum rate of H I photoionization from QSOs at z similar to 3.2, Gamma = 4.8 x 10(-13) s(-1), about half of the total rate inferred through studies of the Ly alpha forest. Therefore, star-forming galaxies and QSOs must contribute comparably to the photoionization of H I in the inter-galactic medium at z similar to 3.