  Quantum oscillation phenomena, in conventional 2-dimensional electron systems
and in the fractional quantum Hall effect, are usually treated in the
Lifshitz-Kosevich formalism. This is justified in three dimensions by
Luttinger's expansion, in the parameter $omega_c/\mu$. We show that in two
dimensions this expansion breaks down, and derive a new expression, exact in
the limit where rainbow graphs dominate the self-energy. Application of our
results to the fractional quantum Hall effect near half-filling shows very
strong deviations from Lifshitz-Kosevich behaviour. We expect that such
deviations will be important in any strongly-interacting 2-dimensional
electronic system.
