  We study the Landau level spectrum of ABA- and ABC-stacked trilayer graphene.
We derive analytic low energy expressions for the spectrum, the validity of
which is confirmed by comparison to a \pi -band tight-binding calculation of
the density of states on the honeycomb lattice. We further study the effect of
a perpendicular electric field on the spectrum, where a zero-energy plateau
appears for ABC stacking order, due to the opening of a gap at the Dirac point,
while the ABA-stacked trilayer graphene remains metallic. We discuss our
results in the context of recent electronic transport experiments. Furthermore,
we argue that the expressions obtained can be useful in the analysis of future
measurements of cyclotron resonance of electrons and holes in trilayer
graphene.
