The study of the pole of the zeta function.

给出了不可交换的正则准齐次向量空间的29种类型，并确定了几乎所有类型的p-进Zeta函数。但尚未确定SL(5)xGL(4)类型的Zeta函数。矢野对这一领域进行了深入的研究，并发表了自己的研究成果。对于它的p-进Zeta函数，我们确定了它的分母中的几个因子。酒井研究了它们，永世研究了几何方面，福井从奇点的角度做了努力。

The totalty of irredeuchible regular Prehomogenous Vector spaces are classified into 29 types.For almost all types, their p-adic zeta functions are determined. But zeta functions for the type SL (5) xGL (4) has not been determined. T.Yano studied in detail for this space, and published a result. For its p-adic zeta functions, we determined several factors in the denominator.Zeta functions are defined for algebraic curves. F.Sakai studied them.M.Nagase studeied geometric aspects, and T.Fukui made an effort from the singularity point of view.