Abstract
Let Q(x) = Q(x(1), x(2), ... , x(n)) be a quadratic form over Z, p be an odd prime. Let V = V-Q = V-pm, denote the set of zeros of Q(x) in Z(pm) and vertical bar V vertical bar denotes the cardinality of V. Set phi(V-pm, y) = Sigma(x is an element of V) e(pm) (x . y) for y not equal 0 and phi(V-pm, y) = vertical bar V-pm vertical bar - p(m(n-1)) for y = 0. In this paper, we shall give a formula for the calculation of the function phi(V, y).