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We present a measurement of the quasar luminosity function in the range0.68<z<4 down to extinction corrected magnitude g_dered=22.5, using a simpleand well understood target selection technique based on the time-variability ofquasars. The completeness of our sample was derived directly from a controlsample of quasars, without requiring complex simulations of quasar light-curvesor colors. A total of 1877 quasar spectra were obtained from dedicated programson the Sloan telescope (as part of the SDSS-III/BOSS survey) and on theMultiple Mirror Telescope. They allowed us to derive the quasar luminosityfunction. It agrees well with previously published results in the redshiftrange 0.68<z<2.6. Our deeper data allow us to extend the measurement to z=4. Wemeasured 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 pureluminosity evolution models, we fitted our LF measurements, and predictedquasar number counts as a function of redshift and observed magnitude. Thesepredictions are useful inputs for future cosmology surveys such as thoserelying on the observation of quasars to measure baryon acoustic oscillations.

Luminosity Function from dedicated SDSS-III and MMT data of quasars in 0.7