2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67485We study the local topological zeta function associated to a complex function that is holomorphic at the origin of C^2 (respectively C^3). We determine all possible poles less than -1/2 (respectively -1). On C^2 our result is a generalization of the fact that the log canonical threshold is never in ]5/6,1[. Similar statements are true for the motivic zeta function.18 pages, to appear in Compositio MathAlgebraic Geometry14B05, 14J17, 32S05 (Primary) 14E15, 14H20 (Secondary)text