  The detection in 10 bursts of an optical counterpart emission (i.e. during
the prompt GRB phase) that is 10-10000 brighter than the extrapolation of the
burst spectrum to optical frequencies suggests a synchrotron self-Compton
origin for the GRB emission, synchrotron producing the optical counterpart
emission. In this model, the second upscattering of the burst photons yields a
prompt GeV-TeV emission, whose brightness depends strongly on an unknown
quantity, the peak energy of the primary synchrotron spectrum. Measurements of
the optical, gamma-ray, and GeV prompt fluxes can be used to test the
synchrotron self-Compton model for GRBs and to determine directly the total
radiative output of GRBs. For a set of 29 GRBs with optical counterpart
detections, we find that the expected GeV photon flux should correlate with the
fluence of the sub-MeV emission and should anticorrelate with the brightness of
the optical counterpart, the strength of these correlations decreasing for an
increasing width of the synchrotron peak energy distribution. The detection of
a GeV prompt emission consistent with the extrapolation of the burst spectrum
to higher energies would rule out the synchrotron self-Compton model if the
sub-MeV burst emission were very bright and the (intrinsic) optical counterpart
were very dim.
