  For special $d$-dimensional hyperbolic shells $E$ with $ d\geq 5$ we show
that the number of lattice points in $E$ intersected with a $d$-dimensional
cube $C_r$ of edge length $r$, can be approximated by the volume of $E\cap
C_r$, as $r$ tends to infinity, up to an error of order ${\mathcal
O}(r^{d-2})$. We generalize results and techniques, used by F. G\"otze (2004),
to a large class of {\em indefinite} quadratic forms and we provide explicit
bounds for the errors in terms of certain Minkowski minima related to these
quadratic forms. Furthermore, we obtain, as in the positive definite case, a
result for multivariate diophantine approximation and for the maximal gap
between values of such indefinite forms.
