  Relativistic quantum plasma dispersion functions are defined and the
longitudinal and transverse response functions for an electron (plus positron)
gas are written in terms of them. The dispersion is separated into
Landau-damping, pair-creation and dissipationless regimes. Explicit forms are
given for the RQPDFs in the cases of a completely degenerate distribution and a
nondegenerate thermal (J\"uttner) distribution. Particular emphasis is placed
on the relation between dissipation and dispersion, with the dissipation
treated in terms of the imaginary parts of RQPDFs. Comparing the dissipation
calculated in this way with the existing treatments leads to the identification
of errors in the literature, which we correct. We also comment on a controversy
as to whether the dispersion curves in a superdense plasma pass through the
region where pair creation is allowed.
