Error terms of density theorems related to prehomogeneous vector spaces

得到与预齐次向量空间相关的密度定理的误差项的问题变得更加清晰。在四次情况下，我们有一个未发表的结果，显示了局部轨道积分的一致估计。然而，为了使用它来达到密度定理的误差项，必须使用包含-排斥原理来显示更准确的估计。为此，我们进行了一些试错。关于Jordan分解概念推广的相关局部理论也取得了一些进展。

Problems for getting the error term of density theorems related to prehomogeneous vector spaces became clearer. In the quartic case, we have an unpublished result showing a uniform estimate of local orbital integrals. However, in order to use it to reach the error term of the density theorem, more accurate estimate has to be shown to use the inclusion-exclusion principle. For that purpose, we carried out some trial and errors. Also there is some progress in the related local theory on the generalization of the notion of Jordan decomposition.