  We have postulated a single pole for the self-energy looking for the
consequences on the one-particle Green function, G(k,w), in the Hubbard model.
We find that G(k,w) satisfies the first two sum rules or moments of Nolting (Z.
Physik 225, 25 (1972)) for any values of the two unknown parameters of the
self-energy. In order to find these two parameters we have used the third and
four sum rules of Nolting. G(k,w) turns out to be identical to the one of
Nolting which is beyond a Hubbard-I solution. Furthermore, we have also
postulated a two-pole Ansatz for the self-energy which is equivalent to a
three-pole ansatz for G(k,w). In the later case, we have fixed two of the
frequencies. This Green function is also beyond the Hubbard-I solution. We
present numerical results for the band structure and the spectral weights.
