Dispersion in a highly relativistic plasma is described by a relativistic p
lasma dispersion function that becomes increasingly sharply peaked as the p
lasma becomes increasingly relativistic. Wave dispersion in a highly relati
vistic plasma is discussed in three contexts: low frequency waves in a puls
ar plasma (a one-dimensional, extremely strongly magnetized, pair plasma),
Langmuir waves in an isotropic thermal plasma, and high-frequency waves in
a synchrotron emitting gas.