Local zeta functions and Newton polyhedra
| dc.creator | Zuniga-Galindo, W. A. | |
| dc.date | 2002-04-19 | |
| dc.date | 2002-12-08 | |
| dc.date.accessioned | 2026-07-07T04:47:48Z | |
| dc.date.available | 2026-07-07T04:47:48Z | |
| dc.description | To a polynomial $f$ over a non-archimedean local field $K$ and a character $χ$ of the group of units of the valuation ring of $K$ one associates Igusa's local zeta function $Z(s,f,χ)$. In this paper, we study the local zeta function $Z(s,f,χ)$ associated to a non-degenerate polynomial $f$, by using an approach based on the p-adic stationary phase formula and Néron p-desingularization. We give a small set of candidates for the poles of $Z(s,f,χ)$ in terms of the Newton polyhedron $ Γ(f)$ of $f$. We also show that for almost all $χ$, the local zeta function $Z(s,f,χ)$ is a polynomial in $q^{-s}$ whose degree is bounded by a constant independent of $χ$. Our second result is a description of the largest pole of $Z(s,f, χ_{\text{triv}})$ in terms of $ Γ(f)$ when the distance between $Γ(f)$ and the origin is at most one. | |
| dc.description | 26 pages, revised version, accepted for publication in Nagoya Math. J | |
| dc.identifier | https://arxiv.org/abs/math/0204241 | |
| dc.identifier | http://arxiv.org/abs/math/0204241 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63858 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11S40, 11D79, 11L05 | |
| dc.title | Local zeta functions and Newton polyhedra | |
| dc.type | text |