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We present new Keck/MOSFIRE K-band spectroscopy for a sample of 14 faint,X-ray-selected active galactic nuclei (AGNs) in the COSMOS field. The datacover the spectral region surrounding the broad Balmer emission lines, whichenables the estimation of black hole masses (M_BH) and accretion rates (interms of L/L_Edd). We focus on 10 AGN at z~3.3, where we observe the Hbetaspectral region, while for the other four z~2.4 sources we use the Halpha broademission line. Compared with previous detailed studies of unobscured AGNs atthese high redshifts, our sources are fainter by an order of magnitude,corresponding to number densities of order ~10^-6--10^-5 Mpc^-3. The lower AGNluminosities also allow for a robust identification of the host galaxyemission, necessary to obtain reliable intrinsic AGN luminosities, BH massesand accretion rates. We find the AGNs in our sample to be powered bysupermassive black holes (SMBHs) with a typical mass of M_BH~5*10^8 M_Sol --significantly lower than the higher-luminosity, rarer quasars reported inprevious studies. The accretion rates are in the range L/L_Edd~0.1-0.5, with anevident lack of sources with lower L/L_Edd (and higher M_BH), as found inseveral studies of faint AGNs at intermediate redshifts. Based on the earlygrowth expected for the SMBHs in our sample, we argue that a significantpopulation of faint z~6 AGNs, with M_BH~10^6 M_Sol, should be detectable in thedeepest X-ray surveys available, but this is not observed. We discuss severalpossible explanations for the apparent absence of such a population, concludingthat the most probable scenario involves an evolution in source obscurationand/or radiative efficiencies.

Faint COSMOS AGN at z~3.3 - I. Black Hole Properties and Constraints on Early Black Hole Growth