On the poles of topological zeta functions

dc.creatorLemahieu, Ann
dc.creatorSegers, Dirk
dc.creatorVeys, Willem
dc.date2005-07-06
dc.date.accessioned2026-07-07T05:21:26Z
dc.date.available2026-07-07T05:21:26Z
dc.descriptionWe 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 P_n := {s_0 | \exists f in C[x_1,..., x_n] : Z_{top,f}(s) has a pole in s_0}. We show that {-(n-1)/2-1/i | i in Z_{>1}} is a subset of P_n; 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 P_n.
dc.identifierhttps://arxiv.org/abs/math/0507121
dc.identifierhttp://arxiv.org/abs/math/0507121
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75693
dc.subjectAlgebraic Geometry
dc.titleOn the poles of topological zeta functions
dc.typetext

Files

Collections