Hard-thermal-loop resummation of the thermodynamics of a hot gluon plasma

We calculate the thermodynamic functions of a hot gluon plasma to leading order in hard-thermal-loop (HTL) perturbation theory. Effects associated with screening, gluon quasiparticles, and Landau damping are resummed to all orders. The ultraviolet divergences generated by the HTL propagator corrections can be canceled by a counterterm that depends on the thermal gluon mass parameter. The HTL thermodynamic functions are compared to those from lattice gauge theory calculations and from quasiparticle models. For reasonable values of the HTL parameters, the deviations from lattice results for $T>\mathrm{}{2T}_c$ have the correct sign and roughly the correct magnitude to be accounted for by next-to-leading order corrections in HTL perturbation theory.