On the poles of Igusa's Local Zeta Function for algebraic sets

Details On the poles of Igusa's Local Zeta Function for algebraic sets On the poles of Igusa's Local Zeta Function for algebraic sets

2003-06-30

arxiv.org/abs/math/0306427v1

Mathematics

Number Theory

11 pages, accepted in Bulletin of the London Mathematical Society

Scientific paper

The aim of this paper is to describe explicitly the poles of the meromorphic continuation of the Igusa local zeta function associated to several polynomials. Using resolution of singularities is possible to express the Igusa's local zeta function as a finite sum of p-adic monomial integrals. We compute these monomial integrals using techniques of toroidal geometry. In this way, we obtain an explicit list for the candidates to poles of the local zeta function associated to several polynomials.

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