  We show that for a class of model Hamiltonians for which certain trial
quantum Hall wavefunctions are exact ground states, there is a single spectral
density function which controls all two-point correlation functions of density,
current and stress tensor components. From this we show that the static
structure factors of these wavefunctions behaves at long wavelengths as $s_4
k^4$ where the coefficient $s_4$ is directly related to the shift:
$s_4=(\mathcal S-1)/8$.
