  Exact relations are derived for the Fermi Hubbard spectral weight function
for infinite U at zero temperature in the thermodynamic limit for any
dimension,any lattice structure and general hopping matrix. These relations
involve moments of the spectral weight function but differ from similar work by
(a) restricting the moments over the interesting low energy (lower Hubbard
band) spectrum and (b) without any of the usual approximations (e.g.
decoupling) for the requisite higher order correlation functions. The latter
are determined exactly as explicit functions of the single particle correlation
function in the infinite U limit. The methods behind these results have the
additional virtue of simplicity - cumbersome, but entirely straightforward. In
a companion paper, the relations offer rich insights into the model behavior
and offer severe tests - a computer lab - of any proposed solution to the
Hubbard model in the strong correlation (large finite U) region. As the
electron density approaches one electron per site, then the correlation
functions become local, so are trivial to compute exactly. In that limit and
for the paramagnetic case, the second central moment of the spectral weight
function is not zero, but quite large.
