Published online by Cambridge University Press: 03 June 2010
We present results from statistical analysis of the largest quasar surveys currently in existence: the Sloan Digital Sky Survey (SDSS), the 2dF QSO Redshift Survey (2QZ), and the 2dF-SDSS LRG and QSO (2SLAQ) Survey. The quasar luminosity function shows highly significant (>99.9%) evidence of downsizing: the number density of faint quasars peaks at lower redshift than bright quasars. We measure the distribution of quasar broad-line widths as a function of luminosity, particularly focusing on the Mg ii λ2799 line. There is a clear trend, such that more luminous quasars show less scatter in line width than fainter quasars. However, the scatter in line width for any given luminosity (particularly in the brightest objects) is so small that it challenges our current understanding of virial black hole mass estimates.