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The local topological zeta function is a rational function associated to agerm of a complex holomorphic function. This function can be computed from anembedded resolution of singularities of the germ. For nondegenerate functionsit is also possible to compute it from the Newton polyhedron. Both ways giverise to a set of candidate poles of the topological zeta function, containingall poles. For plane curves, Veys showed how to filter the actual poles out ofthe candidate poles induced by the resolution graph. In this note we show howto determine from the Newton polyhedron of a nondegenerate plane curve whichcandidate poles are actual poles.

Poles of the topological zeta function for plane curves and Newton polyhedra