  Using recently published estimates - based on high spatial resolution
spectroscopy - of the mass M_{BH} of nuclear black holes for a sample of nearby
galaxies, we explore the dependence of galaxy nucleus emissivity at various
wavelengths on M_{BH}. We confirm an almost linear scaling of the black hole
mass with the baryonic mass of the host spheroidal galaxy. A remarkably tight
relationship is also found with both nuclear and total radio centimetric flux,
with a very steep dependence of the radio flux on M_{BH} (P\propto
M_{BH}^{2.5}). The high-frequency radio power is thus a very good tracer of a
super-massive black hole, and a good estimator of its mass. This, together with
the lack of significant correlations with the low-energy X-ray and far-IR flux,
supports the view that advection-dominated accretion is ruling the energy
output in the low-accretion rate regime. Using the tight dependence of total
radio power on M_{BH} and the rich statistics of radio emission of galaxies, we
derive an estimate of the mass function of remnants in the nearby universe.
This is compared with current models of quasar and AGN activity and of the
origin of the hard X-ray background (HXRB). As for the former, continuous
long-lived AGN activity is excluded by the present data with high significance,
whereas the assumption of a short-lived, possibly recurrent, activity pattern
gives remarkable agreement. The presently estimated black hole mass function
also implies that the HXRB has been produced by a numerous population (\sim
10^{-2} Mpc^{-3}) of moderately massive (M_{BH}\sim 10^7 M_\odot) black holes.
