  In this paper we investigate the distribution of the set of values of a
quadratic form Q, at integral points. In particular we are interested in the
n-point correlations of the this set. The asymptotic behaviour of the counting
function that counts the number of n-tuples of integral points
$\left(v_{1},\dots,v_{n}\right)$, with bounded norm, such that the n-1
differences $Q\left(v_{1}\right)-Q\left(v_{2}\right),\dots
Q\left(v_{n-1}\right)-Q\left(v_{n}\right)$, lie in prescribed intervals is
obtained. The results are valid provided that the quadratic form has rank at
least 5, is not a multiple of a rational form and n is at most the rank of the
quadratic form. For certain quadratic forms satisfying Diophantine conditions
we obtain a rate for the limit. The proofs are based on those in the recent
preprint ([G-M]) of F. G$\"o$tze and G. Margulis, in which they prove an
`effective' version of the Oppenheim Conjecture. In particular, the proofs rely
on Fourier analysis and estimates for certain theta series.
