We present mass functions of distant actively accreting supermassive black holes residing in luminous quasars discovered in the Large Bright Quasar Survey (LBQS), the Bright Quasar Survey (BQS), and the Fall Equatorial Stripe of the Sloan Digital Sky Survey (SDSS). The quasars cover a wide range of redshifts from the local universe to z = 5 and were subject to different selection criteria and flux density limits. This makes these samples complementary and can help us gain additional insight on the true underlying black hole mass distribution free from selection effects and mass estimation errors through future studies. By comparing these quasar samples, we see evidence that the active black hole population at redshift four is somewhat different than that at lower redshifts, including that in the nearby universe. In particular, there is a sharp increase in the space density of the detected active black holes (M BH > ∼ 10 8 M ⊙ ) between redshifts ∼4 and ∼2.5. Also, the mass function of the SDSS quasars at 3.6 ≤ z ≤ 5 has a somewhat flatter high mass-end slope of β = −1.75 ± 0.56, compared to the mass functions based on quasars below z of 3 (BQS and LBQS quasars), which display typical slopes of β ≈ −3.3; the latter are consistent with the mass functions at similar redshifts based on the SDSS Data Release 3 quasar catalog presented by Vestergaard et al. We see clear evidence of cosmic downsizing in the comoving space density distribution of active black holes in the LBQS sample alone. In forthcoming papers, further analysis, comparison, and discussion of these mass functions will be made with other existing black hole mass functions, notably that based on the SDSS DR3 quasar catalog. We present the relationships used to estimate the black hole mass based on the Mg ii emission line; the relations are calibrated to the Hβ and C iv relations by means of several thousand high quality SDSS spectra. Mass estimates of the individual black holes of these samples are also presented.

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We present the mass functions of actively accreting supermassive black holes over the redshift range 0.3 ≤ z ≤ 5 for a well-defined, homogeneous sample of 15,180 quasars from the Sloan Digital Sky Survey Data Release 3 (SDSS DR3) within an effective area of 1644 deg 2 . This sample is the most uniform statistically significant subset available for the DR3 quasar sample. It was used for the DR3 quasar luminosity function, presented by Richards et al., and is the only sample suitable for the determination of the SDSS quasar black hole mass function. The sample extends from i p 15 to i p 19.1 at and to i p 20.2 for . The mass functions display a rise and fall in the space density distribution z Շ 3 z տ 3 of active black holes at all epochs. Within the uncertainties the high-mass decline is consistent with a constant slope of at all epochs. This slope is similar to the bright-end slope of the luminosity function for epochs below b ≈ Ϫ3.3 z p . Our tests suggest that the downturn toward lower mass values is due to incompleteness of the quasar sample with 4 respect to black hole mass. Further details and analysis of these mass functions will be presented in forthcoming papers.

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