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Spin correlations in an interacting electron liquid are studied in thehigh-frequency limit and in both two and three dimensions. The third-moment sumrule is evaluated and used to derive exact limiting forms (at both long- andshort-wavelengths) for the spin-antisymmetric local-field factor, $\lim_{\omega\to \infty}G_-({\bf q, \omega})$. In two dimensions $\lim_{\omega \to\infty}G_-({\bf q, \omega})$ is found to diverge as $1/q$ at long wavelengths,and the spin-antisymmetric exchange-correlation kernel of time-dependent spindensity functional theory diverges as $1/q^2$ in both two and three dimensions.These signal a failure of the local-density approximation, one that can beredressed by alternative approaches.Comment: 5 page

Correlation effects and the high-frequency spin susceptibility of an electron liquid: Exact limits