论文标题
在降低的伯恩斯坦 - 萨托·萨特（Thom-Sebastiani）奇点的多项式上
On the reduced Bernstein-Sato polynomial of Thom-Sebastiani singularities
论文作者
论文摘要
Given two holomorphic functions $f$ and $g$ defined in two respective germs of complex analytic manifolds $(X,x)$ and $(Y,y)$, we know thanks to M. Saito that, as long as one of them is Euler homogeneous, the reduced (or microlocal) Bernstein-Sato polynomial of the Thom-Sebastiani sum $f+g$ can be expressed in terms of those of $ f $和$ g $。在本说明中，我们给出了整个功能方程之间类似关系的纯粹代数证明，该方程可应用于任何可以定义伯恩斯坦 - 摩尔斯坦多项式的设置（不一定是分析）。
Given two holomorphic functions $f$ and $g$ defined in two respective germs of complex analytic manifolds $(X,x)$ and $(Y,y)$, we know thanks to M. Saito that, as long as one of them is Euler homogeneous, the reduced (or microlocal) Bernstein-Sato polynomial of the Thom-Sebastiani sum $f+g$ can be expressed in terms of those of $f$ and $g$. In this note we give a purely algebraic proof of a similar relation between the whole functional equations that can be applied to any setting (not necessarily analytic) in which Bernstein-Sato polynomials can be defined.
