  We perform a detailed analysis of the predictions of resummed perturbation
theory for the pressure and the second-, fourth-, and sixth-order diagonal
quark number susceptibilities in a hot and dense quark-gluon plasma. First, we
present an exact one-loop calculation of the equation of state within
hard-thermal-loop perturbation theory (HTLpt) and compare it to a previous
one-loop HTLpt calculation that employed an expansion in the ratios of thermal
masses and the temperature. We find that this expansion converges reasonably
fast. We then perform a resummation of the existing four-loop weak coupling
expression for the pressure, motivated by dimensional reduction. Finally, we
compare the exact one-loop HTLpt and resummed dimensional reduction results
with state-of-the-art lattice calculations and a recent mass-expanded
three-loop HTLpt calculation.
