  We present detection and analysis of faint X-ray sources in the Chandra deep
field south (CDFS) using the 4 Msec Chandra observation and adopting a new
detection algorithm, based on a targeted search at the position of known high-z
galaxies. This optimized technique results in the identification of 54 z>3
AGNs, 29 of which are new detections. Applying stringent completeness criteria,
we derive AGN luminosity functions in the redshift bins 3-4, 4-5 and >5.8 and
for 42.75<log L(2-10 keV)<44.5. We join this data with the luminous AGN
luminosity functions from optical surveys and find that the evolution of the
high-z, wide luminosity range luminosity function can be best modeled by pure
luminosity evolution with L* decreasing from 6x10^44 ergs/s at z=3 to
L*=2x10^44 ergs/s at z=6. We compare the high-z luminosity function with the
prediction of theoretical models using galaxy interactions as AGN triggering
mechanism. We find that these models are broadly able to reproduce the high-z
AGN luminosity functions. A better agreement is found assuming a minimum Dark
Matter halo mass for black hole formation and growth. We compare our AGN
luminosity functions with galaxy mass functions to derive high-z AGN duty cycle
using observed Eddington ratio distributions to derive black hole masses. We
find that the duty cycle increases with galaxy stellar mass and redshift by a
factor 10-30 from z=0.25 to z=4-5. We also report on the detection of a large
fraction of highly obscured, Compton thick AGN at z>3 (18+17-10%). Their
optical counterparts are not strongly reddened and we thus conclude that the
size of the X-ray absorber is likely smaller than the dust sublimation radius.
We finally report the discovery of a highly star-forming galaxy at z=3.47. If
confirmed, this would be one of the farthest objects in which stellar sources
are detected in X-rays.
