  The high-density electron gas in a strong magnetic field B and at zero
temperature is investigated. The quantum strong-field limit is considered in
which only the lowest Landau level is occupied. It is shown that the
perturbation series of the ground-state energy can be represented in analogy to
the Gell-Mann Brueckner expression of the ground-state energy of the field-free
electron gas. The role of the expansion parameter is taken by $r_B= (2/3 \pi^2)
(B/m^2) (\hbar r_S/e)^3$ instead of the field-free Gell-Mann Brueckner
parameter r_s.
