论文标题
非矩阵Zeta函数的极点函数的极性函数
Poles of Non-Archimedean Zeta Functions for Non-degenerate Rational Functions
论文作者
论文摘要
在本文中，我们研究了当地的Zeta功能，该功能是通过使用基于基于多变量$π$ -ADADIC QUENTARY CHACERAILA $ -ADIC QUATERARY CHACERAILA和new new new new new new new ney new new the Integers $ \ MATHCAL {O} _ {k} $单位的合理功能和特征的任意特征的领域$χ$。当理性函数相对于其牛顿多面体而非分级时，我们就局部Zeta函数给出了明确的公式，并根据牛顿多面体的辅助超平面的正常向量列表，该牛头多面体的正常向量附加了牛顿多面体，该平面附着在newton Policeplan上，该平面附着在newton prowine untical untical untional unteriation and in topation函数。此外，我们获得了一些条件，在这些条件下，通过描述最大的负实极和最小的阳性，与琐碎特征相连的局部ZETA函数至少具有一个真实极。
In this article, we study local zeta functions over non-Archimedean locals fields of arbitrary characteristic attached to rational functions and characters $χ$ of the units of the ring of integers $\mathcal{O}_{K}$, by using an approach based on the multivariate $π$-adic stationary phase formula and Newton polyhedra. When the rational function is non-degenerate with respect to its Newton polyhedron, we give an explicit formula for the local zeta function and a list of the possible poles in terms of the normal vectors of the supporting hyperplanes of the Newton polyhedron attached to the rational function and their expected multiplicities. Furthermore, we obtain some conditions under which the local zeta function attached to the trivial character has at least one real pole by describing the largest negative real pole and the smallest positive one.
