  The charge dynamical response function of the Hubbard model is investigated
on the square lattice in the thermodynamical limit. The obtained charge
excitation spectra consist of a continuum, a gapless collective mode with
anisotropic zero-sound velocity, and a correlation induced high-frequency mode
at $\omega\approx U$. The correlation function is calculated from Gaussian
fluctuations around the paramagnetic saddle-point within the Kotliar and
Ruckenstein slave-boson representation. Its dependence on the on-site Coulomb
repulsion $U$ and density is studied in detail. An approximate analytical
expression of the high frequency mode, that holds for any lattice with one atom
in the unit cell, is derived. Comparison with numerical simulations,
perturbation theory and the polarization potential theory is carried out. We
also show that magnetic instabilities tend to vanish for $T\gtrsim t/6$, and
finite temperature phase diagrams are established.
