  Relativistic shock models of gamma-ray bursts may be tested by comparison of
their predicted low energy asymptotic spectral indices s to observations.
Synchrotron radiation theory predicts that the instantaneous spectrum has s = -
1/3 and the spectrum integrated over the radiative decay of the electrons'
energies has s = 1/2, with other cases lying between these limits. We examine
the spectra of 11 bursts obtained by the Large Area Detectors on BATSE. One
agrees with the predicted instantaneous spectrum, as does the initial portion
of a second, and three are close to the predicted integrated spectrum. All the
observed asymptotic spectral slopes lie in the predicted range. This evidence
for relativistic shocks is independent of detailed models of bursts and of
assumptions about their distances. Radiation observed with the predicted
instantaneous spectrum has a comparatively smooth time dependence, consistent
with the necessarily long radiation time, while that with the predicted
integrated spectrum has a spiky time dependence, consistent with the
necessarily short radiation time.
