The luminosity function of high-redshift QSOs

We measure the luminosity function of QSOs in the redshift range 3.5 < z < 5.2 for the absolute magnitude interval -21 < M_{145} < -28. Suitable criteria are defined to select faint QSOs in the GOODS fields, checking their effectiveness and completeness in detail. The confirmed sample of faint QSOs is compared with a brighter one derived from the SDSS. Using a Monte-Carlo technique we estimate the properties of the luminosity function. Our results show that models based on pure density evolution show better agreement with observation than models based on pure luminosity evolution, even if a different break magnitude with respect to z ~ 2.1 is required at 3.5 < z < 5.2. According to our modeling a faint-end slope steeper than low-redshift observations is required to reproduce the data, moreover models with a steep bright-end slope score a higher probability than models with a bright-end flattening. Determining the faint-end of the luminosity function at these redshifts provides important constraints on models of the joint evolution of galaxies and AGNs.