The most successful explanation proposed for the generation of auroral kilometric radiation (AKR) is the direct cyclotron mechanism in which radiation excited near the local electron cyclotron frequency is amplified through a gyroresonant interaction. Previous work has shown that inclusion of the relativistic mass dependence of the cyclotron frequency is essential to determine the resonant contours in velocity space. In the present work it is demonstrated that relativistic effects can also significantly modify the wave dispersion, even for only mildly relativistic electrons, when &ohgr;pe2/&OHgr;e 2≪1, which is frequently the case in the AKR source region. For a relativistic Maxwellian distribution the R-X mode cutoff is found to be shifted below &OHgr;e for (vte/c)2>2/3 (&ohgr;pe/&OHgr;e)2. Linear analysis of a delta function ring distribution in P⊥ indicates that the R-X mode is unstable for k∥=0 (i.e., propagation perpendicular to the magnetic field) with Re &ohgr;≲&OHgr;e when v/c<&ohgr;pe/&OHgr;e. The effect of finite velocity spread on the maximum growth rate (which occurs for kc/&OHgr;e~1) is minor for k∥=0, while with finite k∥ the maximum growth rate is reduced considerably. The relativistic dispersion effects are found to be significant at propagation angles up to 10¿ away from normal. The addition of a cold electron component produces a new relativistic mode with extraordinary polarization and Re &ohgr;≲&OHgr;e which is unstable for normal and near-normal propagation. Computer simulations using a relativistic electromagnetic particle code indicate that for ring and shell distributions the k∥=0 modes with Re &ohgr;≲&OHgr;e dominate the radiation emission resulting from the cyclotron maser instability. The relativistic dispersion effects should lead to larger growth rates for the generation of AKR than were estimated by cold-plasma calculations either by allowing &ohgr;<&OHgr;e waves to sample all the energy growth regions simultaneously or by allowing &OHgr;e<&ohgr;<&ohgr;x (&ohgr;x is the R-X mode cutoff) waves in the upgoing loss cone to sample regions of velocity space closer to the origin.