  We present results from a statistical analysis of 173 bright radio-quiet AGNs
selected from the Chandra Deep Field-North and Chandra Deep Field-South surveys
(hereafter, CDFs) in the redshift range of 0.1 < z < 4. We find that the X-ray
power-law photon index (Gamma) of radio-quiet AGNs is correlated with their
2-10 keV rest-frame X-ray luminosity (L_X) at the > 99.5 percent confidence
level in two redshift bins, 0.3 < z < 0.96, and 1.5 < z < 3.3 and is slightly
less significant in the redshift bin 0.96 < z < 1.5. We investigate the
redshift evolution of the correlation between the power-law photon index and
the hard X-ray luminosity and find that the slope and offset of a linear fit to
the correlation change significantly (at the > 99.9 percent confidence level)
between redshift bins of 0.3 < z < 0.96 and 1.5 < z < 3.3. We explore physical
scenarios explaining the origin of this correlation and its possible evolution
with redshift in the context of steady corona models focusing on its dependency
on variations of the properties of the hot corona with redshift.
