  We present Very Large Array observations at 1.4 and 5 GHz of a sample of 16
quasi-stellar objects (QSOs) at z = 1.78 to 2.71. Half of the chosen quasars
are bright at mm wavelengths (250 or 350 GHz) while the other half were not
detected at mm wavelengths; the former QSOs were detected at 1.4 GHz, in most
cases at high significance (S/N > ~7), but only three of the latter sources
were detected at radio frequencies, and only at lower significance (S/N ~ 3).
The data are consistent with a correlation between the mm and radio fluxes
indicating a physical connection between the mechanisms responsible for the
radio and mm emission. However, this conclusion is based on data which includes
many upper limits, and deeper observations are clearly needed to verify this
correlation.
  All eight mm detected QSOs are detected in the radio continuum, with radio
flux densities consistent with the radio-to-FIR correlation for low z star
forming galaxies. However, four of these have flatter spectral indices than is
typical for star forming galaxies (i.e. greater than -0.5) suggesting that
radiation from the central AGN dominates the observed radio emission. All the
sources detected at 1.4 GHz are spatially unresolved, with the size limits
typically < 1'' = 6 kpc. High star formation rate galaxies at low redshift are
typically nuclear starbursts, with sizes < 1 kpc. Hence, the current radio size
limits are insufficient to constrain the emission model (AGN or starburst).
