Type: Article
Publication Date: 2015-12-17
Citations: 12
DOI: https://doi.org/10.1515/crelle-2015-0070
Abstract 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.