论文标题
在局部对称空间中膨胀hhosperes的有效等分分布，SO（d）\ sl（d，r） / sl（d，z）（d，z）
Effective equidistribution of expanding horospheres in the locally symmetric space SO(d) \ SL(d,R) / SL(d,Z)
论文作者
论文摘要
我们在扩张的D维椭圆形内（欧几里得计数）和闭合的h旋兰的升降机计数之间使用晶格点计数之间的字典，该链型的计数与半径增加的球相交，以获得两种类型的结果。首先，通过欧几里得计数的$ l^2 $ - 综合误差估计，我们证明了在本地对称空间中扩展houspheres家族的有效等分分配结果，因此（d）\ sl（d，r） / sl（d，d，z）。其次，我们源自欧几里得计数中的均匀误差估计，在SO（D）\ SL（D，D，R）中，计数SL（D，Z）-Orbit点的误差术语（我们称之为截短的嵌合片），以及计算与大径于大的闭合的Horosphere的升降机的数量。
We use a dictionary between lattice point counting inside dilated d-dimensional ellipsoids (Euclidean counting) and counting of lifts of a closed horosphere that intersect a ball of increasing radius, to obtain two types of results. Firstly, via an $L^2$-integral error estimate for Euclidean counting, we prove effective equidistribution results for a family of expanding horospheres in the locally symmetric space SO(d) \ SL(d,R) / SL(d,Z). Secondly, we derive from uniform error estimates in Euclidean counting, error terms for counting SL(d,Z)-orbit points in a certain increasing family of subsets in SO(d) \ SL(d,R) (which we call truncated chimneys), and for counting the number of lifts of a closed horosphere that intersect a ball with large radius.
