The Luminosity Function of high-redshift QSOs - A combined analysis of   GOODS and SDSS
  Aims: In this work the luminosity function of QSOs is measured in the redshift range 3.5<z<5.2 for the absolute magnitude interval -21<M_{145}<-28. The determination of the faint end of the luminosity function at these redshifts provides important constraints on models of joint evolution of galaxies and AGNs. Methods: We have defined suitable criteria to select faint QSOs in the GOODS fields, checking in detail their effectiveness and completeness. Spectroscopic follow-up of the resulting QSO candidates has been carried out. The confirmed sample of faint QSOs is compared with a brighter one derived from the SDSS. We have used a Monte-Carlo technique to estimate the properties of the luminosity function, checking various parameterizations for its shape and evolution. Results: Models based on Pure Density Evolution show better agreement with observation than models based on Pure Luminosity Evolution. However a different break magnitude with respect to z~2.1 is required at 3.5<z<5.2. Models with a steeper faint end score a higher probability. We do not find any evidence for a flattening of the bright end at redshift z>3.5. Conclusions: The estimated space density evolution of QSOs indicates a suppression of the formation and/or feeding of Supermassive Black Holes at these redshifts. The QSO contribution to the UV background is insufficient to ionize the IGM at 3.5<z<5.2. 
F. Fontanot, S. Cristiani, P. Monaco, M. Nonino, E. Vanzella, W.N.   Brandt, A. Grazian, J. Mao