On the poles of topological zeta functions
Résumé
We study the topological zeta function Z top,f (s) associated to a polynomial f with complex coefficients. This is a rational function in one variable and we want to determine the numbers that can occur as a pole of some topological zeta function; by definition these poles are negative rational numbers. We deal with this question in any dimension. Denote Pn := {s0 | ∃f ∈ C[x1,. .. , xn] : Z top,f (s) has a pole in s0}. We show that {−(n−1)/2−1/i | i ∈ Z>1} is a subset of Pn; for n = 2 and n = 3, the last two authors proved before that these are exactly the poles less then −(n − 1)/2. As main result we prove that each rational number in the interval [−(n − 1)/2, 0) is contained in Pn.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)
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