  Recent studies of the cosmic X-ray background (XRB) have suggested the
possible existence of a population of relatively faint sources with hard X-ray
spectra; however, the emission mechanism remains unclear. If the hard X-ray
emission is from the radiatively inefficient, advection dominated accretion
flows (ADAFs) around massive black holes in galactic nuclei, X-ray luminosity
and radio luminosity satisfy the approximate relation $L_R\sim 7\times
10^{35}(\nu/15GHz)^{7/5}(M/10^7M_{\odot}) (L_x/10^{40} erg s^{-1})^{1/10} erg
s^{-1}$ where $L_R=\nu L_\nu$ is the radio luminosity at frequency $\nu$, $M$
is the mass of the accreting black hole, and $10^{40} \simle L_x\simle 10^{42}
erg s^{-1}$ is the 2-10 keV X-ray luminosity. These sources are characterized
by inverted radio spectra $I_\nu \propto \nu^{2/5}$. For example, an ADAF X-ray
source with luminosity $L_x\sim 10^{41} erg s^{-1}$ has a nuclear radio
luminosity of $\sim 4\times 10^{36}(M/3\times 10^7M_{\odot}) erg s^{-1}$ at
$\sim 20$ GHz and if at a distance of $\sim 10 (M/3\times 10^7M_{\odot})^{1/2}
Mpc$ would be detected as a $\sim 1mJy$ point radio source. High frequency
($\sim 20 GHz$), high angular resolution radio observations provide an
important test of the ADAF emission mechanism. Since $L_R$ depends strongly on
black hole mass and only weakly on X-ray luminosity, the successful measurement
of nuclear radio emission could provide an estimate of black hole mass. Because
the X-ray spectra produced by ADAFs are relatively hard, sources of this
emission are natural candidates for contributing to the hard, $>2$ keV,
background.
