正交格的平均分布
Distribution of Shapes of orthogonal Lattices
摘要：
最近Aka，Einsiedler和Shapira证明了，如果d>2，大球面上的本原向量集在其正交补中与d-1维球面上的格形耦合时，在球面与d-1维格形空间的积空间中均匀分布。具体地说，对于d= 3，4，5，假定了一些同余条件.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。
英文摘要：
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.
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