Newton polyhedra and Igusa's local zeta function

Authors
Denef, J Hoornaert, K
Citation
J. Denef et K. Hoornaert, Newton polyhedra and Igusa's local zeta function, J NUMBER TH, 89(1), 2001, pp. 31-64
Citations number
35
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF NUMBER THEORY
ISSN journal
0022314X → ACNP
Volume
89
Issue
1
Year of publication
2001
Pages
31 - 64
Database
ISI
SICI code
0022-314X(200107)89:1<31:NPAILZ>2.0.ZU;2-3
Abstract
We give a very explicit formula for Igusa's local zeta function Z(f)(s) ass ociated to a polynomial f in several variables over the p-adic numbers, whe n f is sufficiently non-degenerated with respect to its Newton polyhedron G amma (f). Using this Formula and the estimates of Adolphson and Sperber on exponential sums over finite fields, we study the largest real pole differe nt from -1 of Z(f)(s) (C) 2001 Academic Press.