Integral points on symmetric varieties and Satake compatifications
Integral points on symmetric varieties and Satake compatifications
复制标题
对称品种和 Satake 配伍上的积分
DOI：
10.1353/ajm.0.0034
复制
发表时间：
2006
影响因子：
1.7
通讯作者：
N. Shah
中科院分区：
文献类型：
--
作者：
A. Gorodnik;H. Oh;N. Shah
设$V$是定义在$\Bbb Q$上的仿射对称簇。我们计算的积分点的角分量的渐近分布在$V$。这个分布是由一个家庭的不变的措施集中在佐竹边界的$V$。在证明过程中，我们描述了一般仿射对称簇的Satake紧化的结构，并计算了模球体积的渐近性。
Let $V$ be an affine symmetric variety defined over $\Bbb Q$. We compute the asymptotic distribution of the angular components of the integral points in $V$. This distribution is described by a family of invariant measures concentrated on the Satake boundary of $V$. In the course of the proof, we describe the structure of the Satake compactifications for general affine symmetric varieties and compute the asymptotic of the volumes of norm balls.