双曲格中的方向
Directions in hyperbolic lattices
摘要：
众所周知，双曲$n$ -空间中的晶格的轨道在径向投影到单位球面上时是均匀分布的。在目前的工作中，我们考虑的投影格点的细尺度统计，并表示的极限分布的随机双曲格。这特别提供了一个新的视角最近的结果博卡，波帕和Zaharescu的2点相关性的模群，并由凯尔默和Kontorovich一般格的尺寸$n=2$。
英文摘要：
It is well known that the orbit of a lattice in hyperbolic $n$-space is uniformly distributed when projected radially onto the unit sphere. In the present work, we consider the fine-scale statistics of the projected lattice points, and express the limit distributions in terms of random hyperbolic lattices. This provides in particular a new perspective on recent results by Boca, Popa, and Zaharescu on 2-point correlations for the modular group, and by Kelmer and Kontorovich for general lattices in dimension $n=2$.
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