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Conclusions
The redshift evolution (from z=0 up to z=3.5) of SMBH mass function can be determined from the joint evolution of X-ray and Radio AGN luminosity functions
Basic ingredient is the mass-LX-LR relationship given by the fundamental plane of black hole activity, that I assumed being redshift-independent
The continuity equation for accretion-driven black holes growth can be integrated bacwards in time using the observationally determined local BHMF as a boundary condition
The results depend on three parameters only: the accretion efficiency, the critical accretion rate separating radiatively efficient from inefficient accretion mode and the X-ray bolometric correction
For all sets of physically motivated parameters, the evolution of the SMBH population between 0<z<3.5 proceed in anti-hierarchical fashion: the BHMF was dominated by higher mass objects at earlier times.
The average accretion rate of the SMBH population also increases with increasing redshift