Purity of exponential sums on $mathbb{A}^n$

[摘要] We give a purity result for two kinds of exponential sums of the type $sum_{xin k^n}psi(f(x))$, where k is a finite field of characteristic p and $psi:ko{mathbb C}^star$ is a non-trivial additive character. In the first case, $fin k[x_1,dots,x_n]$ is a polynomial of degree divisible by p whose highest-degree homogeneous form defines a non-singular projective hypersurface, and in the second case, f is a polynomial of degree prime to p whose highest-degree homogeneous form defines a projective hypersurface with isolated singularities.

[学科分类] 数学（综合）