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According to time-dependent density functional theory, the exactexchange-correlation kernel f$_{xc}$(n, q, $\omega$) determines not only theground-state energy but also the excited-state energies/lifetimes andtime-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 basedupon the satisfaction of exact constraints. For the static ($\omega$ = 0)limit, we modify the model of Constantin and Pitarke at small wavevector q torecover the known second-order gradient expansion, plus other changes. For allfrequencies $\omega$ at q $=$ 0, we use the model of Gross, Kohn, and Iwamoto.A Cauchy integral extends this model to complex $\omega$ and implies thestandard Kramers-Kronig relations. A scaling relation permits closed forms fornot only the imaginary but also the real part of f$_{xc}$ for real $\omega$. Wethen combine these ingredients by damping out the $\omega$ dependence at largeq in the same way that the q dependence is damped. Away from q $=$ 0 and$\omega$ $=$ 0, the correlation contribution to the kernel becomes dominantover exchange, even at r$_s$ $=$ 4, the valence electron density of metallicsodium. The resulting correlation energy from integration over imaginary$\omega$ is essentially exact. The plasmon pole of the density responsefunction is found by analytic continuation of f$_{xc}$ to $\omega$ just belowthe real axis, and the resulting plasmon lifetime first decreases from infinityand then increases as q grows from 0 toward the electron-hole continuum. Astatic charge-density wave is found for r$_s$ $>$ 69, and shown to beassociated with softening of the plasmon mode. The exchange-only version of ourstatic kernel confirms Overhauser's 1968 prediction that correlation enhancesthe charge-density wave.

Constraint-based Wavevector- and Frequency-dependent Exchange-Correlation Kernel of the Uniform Electron Gas