Fonctions d’Igusa p-adiques, polynômes de Bernstein, et polyèdres de Newton. (p-adic Igusa functions, Bernstein polynomials and Newton polyhedra). (French) Zbl 0713.11083

Loeser, François

J. Reine Angew. Math. 412, 75-96 (1990).

In this paper we prove that the real parts of the poles of the p-adic Igusa local zeta function attached to a polynomial which is non degenerate for its Newton polyhedron are always roots of the Bernstein polynomial, under a mild technical condition on the polyhedron. One of the main tool is a toroidal version of a non-vanishing theorem of H. Esnault and E. Viehweg [ibid. 381, 211-213 (1987; Zbl 0619.14006)].

Reviewer: F.Loeser

MSC:

11S40	Zeta functions and \(L\)-functions
12H25	\(p\)-adic differential equations
14M25	Toric varieties, Newton polyhedra, Okounkov bodies

Keywords:

p-adic Igusa local zeta function; Newton polyhedron; Bernstein polynomial