2014/09/12 by Jens Marklof, Marklof, Jens, Ilya Vinogradov +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #math.DS #math.NT
paper · pdf · doi:10.48550/arxiv.1409.3764
22 pages
arxiv created 2015/09/02 · arxiv updated 2015/09/03
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.