  We show that the expression of the high-density (i.e small-$r_s$) correlation
energy per electron for the one-dimensional uniform electron gas can be
obtained by conventional perturbation theory and is of the form $\Ec(r_s) =
-\pi^2/360 + 0.00845 r_s + ...$, where $r_s$ is the average radius of an
electron. Combining these new results with the low-density correlation energy
expansion, we propose a local-density approximation correlation functional,
which deviates by a maximum of 0.1 millihartree compared to the benchmark DMC
calculations.
