  Wave dispersion in a pulsar plasma is discussed emphasizing the relevance of
different inertial frames, notably the plasma rest frame ${\cal K}$ and the
pulsar frame ${\cal K}'$ in which the plasma is streaming with speed
$\beta_{\rm s}$. The effect of a Lorentz transformation on both subluminal,
$|z|<1$, and superluminal, $|z|>1$, waves is discussed. It is argued that the
preferred choice for a relativistically streaming distribution should be a
Lorentz-transformed J\"uttner distribution; such a distribution is compared
with other choices including a relativistically streaming Gaussian
distribution. A Lorentz transformation of the dielectric tensor is written
down, and used to derive an explicit relation between the relativistic plasma
dispersion functions in ${\cal K}$ and ${\cal K}'$. It is shown that the
dispersion equation can be written in an invariant form, implying a one-to-one
correspondence between wave modes in any two inertial frames. Although there
are only three modes in the plasma rest frame, it is possible for
backward-propagating or negative-frequency solutions in ${\cal K}$ to transform
into additional forward-propagating, positive-frequency solutions in ${\cal
K}'$ that may be regarded as additional modes.
