The magnetized electron gas in terms of Hurwitz zeta functions Original Research Article

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.