Moments of the ARPES spectral function of an undoped Mott insulator

We derive analytic expressions for the first three frequency moments of the single particle spectral function for one hole in a Mott insulator in terms of equilibrium spin correlation functions of the insulating state. We show that the ``remnant Fermi surface`` detected in ARPES experiments is, in fact, a reflection of the strong antiferromagnetic correlations of the system, {\it not} a reflection of the original band-structure Fermi surface. We suggest that ARPES data could be used to measure the magnetic specific heat.