Purity of exponential sums on An, II

Abstract

We give a purity result for exponential sums of the type P x∈kn ψ(f(x)), where k is a finite field of characteristic p, ψ : k → C* is a non-trivial additive character and f ∈ k[x1, . . . , xn] is a polynomial whose highest degree homogeneous form splits as a product of factors defining a divisor with normal crossings in P n−1.