  The XLF of AGN offers a robust tool to study the evolution and the growth of
SMBHs over cosmic time. Owing to the limited area probed by X-ray surveys,
optical surveys are routinely used to probe the accretion in the high redshift
Universe $z\geq 3$. However, optical surveys may be incomplete because they are
strongly affected by dust redenning. In this work, we derive the XLF and its
evolution at high redshifts using a large sample of AGNs selected in different
fields with various areas and depths covering a wide range of luminosities.
Additionally, we put the tightest yet constraints on the absorption function in
this redshift regime. In particular, we use more than 600 soft X-ray selected
high-z sources in the Chandra Deep fields, the Chandra COSMOS Legacy survey and
the XMM-XXL northern field. We derive the X-ray spectral properties for all
sources via spectral fitting, using a consistent technique and model. For
modeling the parametric form of the XLF and the absorption function, we use a
Bayesian methodology allowing us to correctly propagate the uncertainties for
the observed X-ray properties of our sources and also the absorption effects.
The evolution of XLF is in agreement with a pure density evolution model
similar to what is witnessed at optical wavelengths, although a luminosity
dependent density evolution model cannot be securely ruled out. A large
fraction ($60\%)$ of our sources are absorbed by column densities of $\rm N_H
\geq 10^{23} cm^{-2} $, while $17$\% of the sources are CTK. Our results favor
a scenario where both the ISM of the host and the AGN torus contribute to the
obscuration. The derived BHAD is in agreement with the simulations, if one
takes into account that the X-ray AGN are hosted by massive galaxies, while it
differs from the one derived using JWST data. The latter could be due to the
differences in the AGN and host-galaxy properties.
