The SDSS-III Baryon Oscillation Spectroscopic Survey: The Quasar
  Luminosity Function from Data Release Nine
  We present a new measurement of the optical Quasar Luminosity Function (QLF),
using data from the Sloan Digital Sky Survey-III: Baryon Oscillation
Spectroscopic Survey (SDSS-III: BOSS). From the SDSS-III Data Release Nine
(DR9), we select a uniform sample of 22,301 i<=21.8 quasars over an area of
2236 sq. deg with confirmed spectroscopic redshifts between 2.2<z<3.5, filling
in a key part of the luminosity-redshift plane for optical quasar studies. We
derive the completeness of the survey through simulated quasar photometry, and
check this completeness estimate using a sample of quasars selected by their
photometric variability within the BOSS footprint. We investigate the level of
systematics associated with our quasar sample using the simulations, in the
process generating color-redshift relations and a new quasar k-correction. We
probe the faint end of the QLF to M_i(z=2.2) = -24.5 and see a clear break in
the QLF at all redshifts up to z=3.5. We find that a log-linear relation (in
log[Phi*] - M*) for a luminosity and density evolution (LEDE) model adequately
describes our data within the range 2.2<z<3.5; across this interval the break
luminosity increases by a factor of ~2.3 while Phi* declines by a factor of ~6.
At z<2.2 our data is reasonably well fit by a pure luminosity evolution (PLE)
model. We see only a weak signature of "AGN downsizing", in line with recent
studies of the hard X-ray luminosity function. We compare our measured QLF to a
number of theoretical models and find that models making a variety of
assumptions about quasar triggering and halo occupation can fit our data over a
wide range of redshifts and luminosities.
