On spinor exceptional representations

Abstract

Let f(x1 …, xm) be a quadratic form with integer coefficients and c ∈ Z. If f(x) = c has a solution over the real numbers and if f(x) ≡ c (mod N) is soluble for every modulus N, then at least some form h in the genus of f represents c. If m ≧ 4 one may further conclude that h belongs to the spinor genus of f. This does not hold when m = 3.