  We present a simple scheme to evaluate linear response functions including
quantum fluctuation corrections on top of the Gutzwiller approximation. The
method is derived for a generic multi-band lattice Hamiltonian without any
assumption about the dynamics of the variational correlation parameters that
define the Gutzwiller wavefunction, and which thus behave as genuine dynamical
degrees of freedom that add on those of the variational uncorrelated Slater
determinant. We apply the method to the standard half-filled single-band
Hubbard model. We are able to recover known results, but, as by-product, we
also obtain few novel ones. In particular, we show that quantum fluctuations
can reproduce almost quantitatively the behaviour of the uniform magnetic
susceptibility uncovered by dynamical mean field theory, which, though enhanced
by correlations, is found to be smooth across the paramagnetic Mott transition.
By contrast, the simple Gutzwiller approximation predicts that susceptibility
to diverge at the transition.
