  Finding the sources responsible for the hydrogen reionization is one of the
most pressing issues in cosmology. Bright QSOs are known to ionize their
surrounding neighborhood, but they are too few to ensure the required HI
ionizing background. A significant contribution by faint AGNs, however, could
solve the problem, as recently advocated on the basis of a relatively large
space density of faint active nuclei at z>4. We have carried out an exploratory
spectroscopic program to measure the HI ionizing emission of 16 faint AGNs
spanning a broad U-I color interval, with I~21-23 and 3.6<z<4.2. These AGNs are
three magnitudes fainter than the typical SDSS QSOs (M1450<~-26) which are
known to ionize their surrounding IGM at z>~4. The LyC escape fraction has been
detected with S/N ratio of ~10-120 and is between 44 and 100% for all the
observed faint AGNs, with a mean value of 74% at 3.6<z<4.2 and
-25.1<M1450<-23.3, in agreement with the value found in the literature for much
brighter QSOs (M1450<~-26) at the same redshifts. The LyC escape fraction of
our faint AGNs does not show any dependence on the absolute luminosities or on
the observed U-I colors. Assuming that the LyC escape fraction remains close to
~75% down to M1450~-18, we find that the AGN population can provide between 16
and 73% (depending on the adopted luminosity function) of the whole ionizing UV
background at z~4, measured through the Lyman forest. This contribution
increases to 25-100% if other determinations of the ionizing UV background are
adopted. Extrapolating these results to z~5-7, there are possible indications
that bright QSOs and faint AGNs can provide a significant contribution to the
reionization of the Universe, if their space density is high at M1450~-23.
