On the Poles of Igusa’s Local Zeta Function for Algebraic Sets
نویسنده
چکیده
Abstract. Let K be a p−adic field, and ZΦ(s, f), s ∈ C, with Re(s) > 0, the Igusa local zeta function associated to f(x) = (f1(x), .., fl(x)) ∈ [K (x1, .., xn)] , and Φ a Schwartz-Bruhat function. The aim of this paper is to describe explicitly the poles of the meromorphic continuation of ZΦ(s, f). Using resolution of singularities is possible to express ZΦ(s, f) as a finite sum of p−adic monomial integrals. These monomial integrals are computed explicitly by using techniques of toroidal geometry. In this way, an explicit list for the candidates to poles of ZΦ(s, f) is obtained.
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