Abstract
Let Q (x) = Q (x(1),x(2),...,x(n)) be a quadratic form in n variables with integer coefficients, p an odd prime and Z(p) the integers (mod p). We obtain bounds on the number of solutions over Z(p) to the congruence Q (x) 0 (mod p) in a general rectangular box. We use Fourier series and exponential sums to obtain our results.