On positive definite quadratic forms

We consider real positive definite quadratic forms Q(x) with algebraic coef ficients. Suppose that the ratios of the coefficients of Q(x) are not all r ational. It is shown that there is a number so such that if s greater than or equal to s(0), then for any positive epsilon there is a number M-o(epsil on) such that for all M greater than or equal to M-0(epsilon), there exists an integral vector x with \ Q(x) - M \ < epsilon. That is, the gaps betwee n values of such a form at integral points tend to zero as the values tend to infinity. In fact we may take s(0) = 416. We note that the author has re cently discovered that a stronger result than this has been given by other workers, but proved with a different method.