  We obtain explicit expressions for thermodynamic quantities of a relativistic
degenerate free electron gas in a magnetic field in terms of Hurwitz Zeta
functions. The formulation allows for systematic expansion in all regimes.
Three energy scales appear naturally in the degenerate relativistic gas: the
Fermi energy Ef, the temperature T and an energy related to the magnetic field
or Landau level spacing, eB/Ef. We study the cold and warm scenarios, T <<
eB/Ef and eB/Ef << T, respectively. We reproduce the oscillations of the
magnetization as a function of the field in the cold regime and the dilution of
them in the warm regime.
