  We study the consequences of long-range Coulomb interactions at the critical
points between integer/fractional quantum Hall states and an insulator. We use
low energy theories for such transitions in anyon gases in the presence of an
external periodic potential. We find that Coulomb interactions are marginally
irrelevant for the integer quantum Hall case. For the fractional case,
depending upon the anyon statistics parameter, we find behavior similar to the
integer case, or flow to a novel line of fixed points with exponents $z=1$,
$\nu > 1$ stable against weak disorder in the position of the critical point,
or run-away flow to strong coupling.
