标题： 平面曲线的拓扑Zeta函数的极点与牛顿多面体 显示英文标题

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

摘要： 局部拓扑zeta函数是一个与复解析函数的芽相关的有理函数。 该函数可以从该芽的奇点的嵌入解析解来计算。 对于非退化函数，也可以从牛顿多面体来计算它。 这两种方法都会产生一组候选极点，包含所有极点。 对于平面曲线，Veys展示了如何从解析图引起的候选极点中筛选出实际的极点。 在本文中，我们展示了如何从非退化平面曲线的牛顿多面体中确定哪些候选极点是实际的极点。 显示英文摘要

摘要： The local topological zeta function is a rational function associated to a germ of a complex holomorphic function. This function can be computed from an embedded resolution of singularities of the germ. For nondegenerate functions it is also possible to compute it from the Newton polyhedron. Both ways give rise to a set of candidate poles of the topological zeta function, containing all poles. For plane curves, Veys showed how to filter the actual poles out of the candidate poles induced by the resolution graph. In this note we show how to determine from the Newton polyhedron of a nondegenerate plane curve which candidate poles are actual poles.