  We investigate magento-oscillations in the specific heat of non-relativistic
fermions with a Fermi surface minimally coupled to a fluctuating U(1) gauge
field. Our study is motivated by the recent observation of quantum oscillations
in the underdoped cuprates, and by theoretical models of pocket Fermi surfaces
realizing a non-Fermi liquid `algebraic charge liquid'. Our main result is the
computation of the order 1/N correction to the Lifshitz-Kosevich expression for
the oscillation amplitude in the dirty limit in a model with N species of
fermions.
