Distribution of shapes of orthogonal lattices
Distribution of shapes of orthogonal lattices
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正交晶格的形状分布
DOI：
10.1017/etds.2017.78
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发表时间：
2016
影响因子：
0.9
通讯作者：
Philipp Wirth
中科院分区：
文献类型：
--
作者：
M. Einsiedler;René Rühr;Philipp Wirth
最近Aka，Einsiedler和Shapira证明了，如果d>2，大球面上的本原向量集在投影到d-1维球面上时，与其正交补的格形耦合，在球面与d-1维格形空间的乘积空间中等分布。具体地说，对于$d= 3，4，5 $，假设了一些同余条件。通过使用幂幺流理论的最新进展，我们有效的动力学证明，以消除这些条件为$d= 4，5 $。它还遵循，均匀分布发生与多项式误差项相对于原始点的长度。
It was recently shown by Aka, Einsiedler and Shapira that if $d>2$ , the set of primitive vectors on large spheres when projected to the $(d-1)$ -dimensional sphere coupled with the shape of the lattice in their orthogonal complement equidistribute in the product space of the sphere with the space of shapes of $(d-1)$ -dimensional lattices. Specifically, for $d=3,4,5$ some congruence conditions are assumed. By using recent advances in the theory of unipotent flows, we effectivize the dynamical proof to remove those conditions for $d=4,5$ . It also follows that equidistribution takes place with a polynomial error term with respect to the length of the primitive points.