### abstract

- The properties of a relativistic plasma dispersion function (RPDF) for an intrinsically extremely relativist, strongly magnetized, one-dimensional, electron[right angle bracket] [dbl greater-than sign] 1 in its rest frame, the RPDF has a large peak >[left angle bracket][right angle bracket] below the speed of light, and the asymptotic value (infinite phase speed) is [left angle bracket]3[right angle bracket] [similar] 1/[left angle bracket]γ[right angle bracket]. These features are not particularly sensitive to the choice of distribution function. The RPDF is used to discuss the properties of waves in such plasmas. Particular points discussed are the implications of the RPDF for the maximum frequency for parallel Langmuir waves, and for the reconnection between the Langmuir mode and the Alfvén mode.