  We use a dispersion relation in conjunction with the operator product
expansion (OPE) to derive model independent sum rules for the dynamic structure
functions of systems with large scattering lengths. We present an explicit sum
rule for the structure functions that control the density and spin response of
the many-body ground state. Our methods are general, and apply to either
fermions or bosons which interact through two-body contact interactions with
large scattering lengths. By employing a Borel transform of the OPE, the
relevant integrals are weighted towards infrared frequencies, thus allowing for
greater overlap low energy data. Similar sum rules can be derived for other
response functions. The sum rules can be used to extract the contact parameter
introduced by Tan, including universality violating corrections at finite
scattering lengths.
