Zeta Functions for Analytic Mappings, Log-principalization of Ideals, and Newton Polyhedra
| dc.creator | Veys, Willem | |
| dc.creator | Zuniga-Galindo, W. A. | |
| dc.date | 2006-01-13 | |
| dc.date | 2006-09-08 | |
| dc.date.accessioned | 2026-07-07T06:58:54Z | |
| dc.date.available | 2026-07-07T06:58:54Z | |
| dc.description | In this paper we provide a geometric description of the possible poles of the Igusa local zeta function associated to an analytic mapping and a locally constant function, in terms of a log-principalizaton of an ideal naturally attached to the mapping. Typically our new method provides a much shorter list of possible poles compared with the previous methods. We determine the largest real part of the poles of the Igusa zeta function, and then as a corollary, we obtain an asymptotic estimation for the number of solutions of an arbitrary system of polynomial congruences in terms of the log-canonical threshold of the subscheme given by the ideal attached to the mapping. We associate to an analytic mapping a Newton polyhedron and a new notion of non-degeneracy with respect to it. By constructing a log-principalization, we give an explicit list for the possible poles of the Igusa zeta function associated to a non-degenerate mapping. | |
| dc.description | Some typos were corrected. To appear in Trans. Amer. Math. Soc | |
| dc.identifier | https://arxiv.org/abs/math/0601336 | |
| dc.identifier | http://arxiv.org/abs/math/0601336 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107544 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | Primary 11S40, 11D79, 14M25; Secondary 32S45 | |
| dc.title | Zeta Functions for Analytic Mappings, Log-principalization of Ideals, and Newton Polyhedra | |
| dc.type | text |