The XMM-Newton Serendipitous Survey. VI. The X-ray Luminosity Function
  We present the X-ray luminosity function of AGN in three energy bands (Soft: 0.5-2 keV, Hard: 2-10 keV and Ultrahard: 4.5-7.5 keV). We have used the XMS survey along with other highly complete flux-limited deeper and shallower surveys for a total of 1009, 435 and 119 sources in the Soft, Hard and Ultrahard bands, respectively. We have modeled the intrinsic absorption of the Hard and Ultrahard sources (NH function) and computed the intrinsic X-ray luminosity function in all bands using a Maximum Likelihood fit technique to an analytical model. We find that the X-ray luminosity function (XLF) is best described by a Luminosity-Dependent Density Evolution (LDDE) model. Our results show a good overall agreement with previous results in the Hard band, although with slightly weaker evolution. Our model in the Soft band present slight discrepancies with other works in this band, the shape of our present day XLF being significantly flatter. We find faster evolution in the AGN detected in the Ultrahard band than those in the Hard band. The fraction of absorbed AGN in the Hard and Ultrahard bands is dependent on the X-ray luminosity. We find evidence of evolution of this fraction with redshift in the Hard band but not in the Ultrahard band, possibly due to the low statistics. Our best-fit XLF shows that the high-luminosity AGN are fully formed earlier than the less luminous AGN. The latter sources account for the vast majority of the accretion rate and mass density of the Universe, according to an anti-hierarchical black hole growth scenario. 
J. Ebrero, F.J. Carrera, M.J. Page, J.D. Silverman, X. Barcons, M.T.   Ceballos, A. Corral, R. Della Ceca and M.G. Watson