Abstract

We give an explicit description of the poles of the Igusa local zeta function associated to a polynomial mapping g, in the case in which it is a nondegenerate homogeneous mapping of degree d. The proof uses a generalization of the p-adic stationary phase formula and Néron p-desingularization.

Keywords

local zeta function, polynomial mappings, p-adic stationary formula, congruences in many variables

Mathematical Subject Classification

Primary: 11S40, 11D79

Authors