论文标题
在Igusa局部ZETA功能上
On Igusa local zeta functions of Hauser hybrid polynomials
论文作者
论文摘要
令$ k $为本地字段，$ f（x）\在k [x] $中为非恒定多项式。当$ {\ rm char} k = 0 $时，igusa显示局部zeta函数是一个合理的函数。但是，当$ {\ rm char} k> 0 $时，本地Zeta函数的合理性一般是未知的。在本文中，我们研究了三个变量中所谓的杂种多项式的局部Zeta函数，该变量具有在非架构的阳性特征局部领域中的系数。这些杂种多项式首先是由Hauser在2003年引入的，以研究呈阳性特征中奇异性的分辨率。我们建立了这些局部Zeta函数的理性定理，并明确列出所有候选杆。我们的结果概括了Le $ \ cucute {o} $ n-cardenal，ibadula和segers以及Yin和Hong的工作。
Let $K$ be a local field and $f(x)\in K[x]$ be a non-constant polynomial. When ${\rm char}K=0$, Igusa showed the local zeta function is a rational function. However, when ${\rm char}K>0$, the rationality of the local zeta function is unknown in general. In this paper, we study the local zeta functions for the so-called hybrid polynomials in three variables with coefficients in a non-archimedean local field of positive characteristic. These hybrid polynomials were first introduced by Hauser in 2003 to study the resolution of singularities in positive characteristic. We establish the rationality theorem for these local zeta functions and list explicitly all the candidate poles. Our result generalizes the work of Le$\acute{o}$n-Cardenal, Ibadula and Segers and that of Yin and Hong.
