  According to time-dependent density functional theory, the exact
exchange-correlation kernel f$_{xc}$(n, q, $\omega$) determines not only the
ground-state energy but also the excited-state energies/lifetimes and
time-dependent linear density response of an electron gas of uniform density n
$=$ 3/(4$\pi$r$^3_s$). Here we propose a parametrization of this function based
upon the satisfaction of exact constraints. For the static ($\omega$ = 0)
limit, we modify the model of Constantin and Pitarke at small wavevector q to
recover the known second-order gradient expansion, plus other changes. For all
frequencies $\omega$ at q $=$ 0, we use the model of Gross, Kohn, and Iwamoto.
A Cauchy integral extends this model to complex $\omega$ and implies the
standard Kramers-Kronig relations. A scaling relation permits closed forms for
not only the imaginary but also the real part of f$_{xc}$ for real $\omega$. We
then combine these ingredients by damping out the $\omega$ dependence at large
q in the same way that the q dependence is damped. Away from q $=$ 0 and
$\omega$ $=$ 0, the correlation contribution to the kernel becomes dominant
over exchange, even at r$_s$ $=$ 4, the valence electron density of metallic
sodium. The resulting correlation energy from integration over imaginary
$\omega$ is essentially exact. The plasmon pole of the density response
function is found by analytic continuation of f$_{xc}$ to $\omega$ just below
the real axis, and the resulting plasmon lifetime first decreases from infinity
and then increases as q grows from 0 toward the electron-hole continuum. A
static charge-density wave is found for r$_s$ $>$ 69, and shown to be
associated with softening of the plasmon mode. The exchange-only version of our
static kernel confirms Overhauser's 1968 prediction that correlation enhances
the charge-density wave.
