Loeser, François 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 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 Cited in 19 Documents 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 PDF BibTeX XML Cite \textit{F. Loeser}, J. Reine Angew. Math. 412, 75--96 (1990; Zbl 0713.11083) Full Text: DOI Crelle EuDML