  The ground-state energy of a three-dimensional polaron gas in a magnetic
field is investigated. An upper bound for the ground-state energy is derived
within a variational approach which is based on a many-body generalization of
the Lee-Low-Pines transformation. The basic contributing ingredients found are
the ground-state energy and the static structure factor of the homogeneous
electron gas in a magnetic field. Both these quantities are derived in the
Hartree-Fock approximation. The resulting ground-state energy of the polaron
gas is analyzed as a function of the electron density and of the magnetic field
strength.
