Directions in hyperbolic lattices

被引：12

作者：

Marklof, Jens ^{[1
]}

Vinogradov, Ilya ^{[1
]}

机构：

[1] Univ Bristol, Sch Math, Bristol BS8 1TW, Avon, England

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2018年 / 740卷

基金：

欧洲研究理事会;

关键词：

PAIR CORRELATION; EQUIDISTRIBUTION; ANGLES;

D O I：

10.1515/crelle-2015-0070

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：161 / 186

页数：26

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