We present a measurement of the quasar luminosity function in the range 0.68 < z < 4 down to extinction corrected magnitude g _ { dered } = 22.5 , using a simple and well understood target selection technique based on the time-variability of quasars .
The completeness of our sample was derived directly from a control sample of quasars , without requiring complex simulations of quasar light-curves or colors .
A total of 1877 quasar spectra were obtained from dedicated programs on the Sloan telescope ( as part of the SDSS-III/BOSS survey ) and on the Multiple Mirror Telescope .
They allowed us to derive the quasar luminosity function .
It agrees well with results previously published in the redshift range 0.68 < z < 2.6 .
Our deeper data allow us to extend the measurement to z = 4 .
We measured quasar densities to g _ { dered } < 22.5 , obtaining 30 QSO per { deg } ^ { 2 } at z < 1 , 99 QSO per deg ^ { 2 } for 1 < z < 2.15 , and 47 QSO per deg ^ { 2 } at z > 2.15 .
Using pure luminosity evolution models , we fitted our LF measurements and predicted quasar number counts as a function of redshift and observed magnitude .
These predictions are useful inputs for future cosmology surveys such as those relying on the observation of quasars to measure baryon acoustic oscillations .