Three-loop HTL gluon thermodynamics at intermediate coupling

We calculate the thermodynamic functions of pure-glue QCD to three-loop order using the hard-thermal-loop perturbation theory (HTLpt) reorganization of finite temperature quantum field theory. We show that at three-loop order hard-thermal-loop perturbation theory is compatible with lattice results for the pressure, energy density, and entropy down to temperatures T similar or equal to 3 T-c. Our results suggest that HTLpt provides a systematic framework that can be used to calculate static and dynamic quantities for temperatures relevant at LHC.