  We apply the operator-product expansion to determine the asymptotic form of
the current response of a Fermi gas in two and three dimensions. The
leading-order term away from the one-particle peak is proportional to a
quantity known as the contact, the coefficient of which is determined exactly.
We also calculate the dynamic structure factor and the high-frequency tails of
the spectral viscosities as a function of the scattering length. Our results
are used to derive certain sum rules for the viscosities.
