Newton stratification for polynomials: The open stratum Original Research Article

In this paper we consider the Newton polygons of L-functions coming from additive exponential sums associated to a polynomial over a finite field image. These polygons define a stratification of the space of polynomials of fixed degree. We determine the open stratum: we give the generic Newton polygon for polynomials of degree dgreater-or-equal, slanted2 when the characteristic pgreater-or-equal, slanted3d, and the Hasse polynomial over image, i.e. the equation defining the hypersurface complementary to the open stratum.