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We show that for a class of model Hamiltonians for which certain trialquantum Hall wavefunctions are exact ground states, there is a single spectraldensity function which controls all two-point correlation functions of density,current and stress tensor components. From this we show that the staticstructure factors of these wavefunctions behaves at long wavelengths as $s_4k^4$ where the coefficient $s_4$ is directly related to the shift:$s_4=(\mathcal S-1)/8$.

Lowest Landau Level Stress Tensor and Structure Factor of Trial Quantum Hall Wave Functions