Hardy's theorem for zeta-functions of quadratic forms

Let Q(u(1), ..., u(t))=Sigma d(ij)u(i)u(j) (i, j=1 to l) be a positive definite quadratic form in l(greater than or equal to 3) variables with integer coefficients d(ij)(=d(jl)). Put s=sigma+it and for sigma>(l/2) write Z(Q)(s)=Sigma'(Q(u(1), ..., u(l)))(-s), where the accent indicates that the sum is over all l-tuples of integers (u(1), ..., u(l)) with the exception of (0, ..., 0). It is well-known that this series converges for sigma>(l/2) and that (s-(l/2))Z(Q)(s) can be continued to an entire function of s. Let delta be any constant with 0<delta<1/100. Then it is proved that Z(Q)(s) has >>delta TlogT zeros in the rectangle (\sigma-1/2\less than or equal to delta, T less than or equal to t less than or equal to 2T).