On spinor exceptional representations

Abstract

Let f(x 1 …, x m ) 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.