论文标题
Shintani Zeta功能和牛顿多型的杆结构
Pole structure of Shintani zeta functions and Newton polytopes
论文作者
论文摘要
众所周知，概括多个Zeta函数的Shintani Zeta函数扩展到具有仿射超平面上的杆子的Meromormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormorplanes。我们完善了这一结果，表明杆子位于与Shintani Zeta功能定义矩阵相关的某些凸Polyhedra平行的超平面上。明确地，后者是由基础矩阵的列诱导的多项式的牛顿多面体。然后，我们证明了在规范基础上描述超平面的方程式的系数为零或一个，类似于恢复通用的Feynman振幅时产生的极点。为此，我们引入了一种算法以在图上分配重量，以使每个顶点的重量满足给定的下限。
It is known that Shintani zeta functions, which generalise multiple zeta functions, extend to meromorphic functions with poles on affine hyperplanes. We refine this result in showing that the poles lie on hyperplanes parallel to the facets of certain convex polyhedra associated to the defining matrix for the Shintani zeta function. Explicitly, the latter are the Newton polytopes of the polynomials induced by the columns of the underlying matrix. We then prove that the coefficients of the equation which describes the hyperplanes in the canonical basis are either zero or one, similar to the poles arising when renormalising generic Feynman amplitudes. For that purpose, we introduce an algorithm to distribute weight over a graph such that the weight at each vertex satisfies a given lower bound.
