Local zeta function for nondegenerate homogeneous mappings

W. A. Zuniga-Galindo

Vol. 218 (2005), No. 1, 187–200

DOI: 10.2140/pjm.2005.218.187

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 2000

Primary: 11S40, 11D79

Milestones

Received: 27 December 2002

Published: 1 January 2005