The magnetized electron gas in terms of Hurwitz zeta functions

We obtain explicit expressions for thermodynamic quantities of a relativist ic degenerate free electron gas in a magnetic field in terms of Hurwitz zet a functions. The formulation allows for systematic expansion in all regimes . Three energy scales appear naturally in the degenerate relativistic gas: the Fermi energy E-F, the temperature T and an energy related to the magnet ic field or Landau level spacing, eB/E-F. We study the cold and warm scenar ios, T much less than eB/E-F and eB/E-F much less than 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. (C) 2001 El sevier Science B.V. All: rights reserved.