Directions in hyperbolic lattices

Jens Marklof, Ilya Vinogradov

Research output: Contribution to journalArticle (Academic Journal)peer-review

7 Citations (Scopus)
262 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)161-186
Number of pages26
JournalJournal für die reine und angewandte Mathematik
Issue number740
Early online date17 Dec 2015
Publication statusPublished - Jul 2018


Dive into the research topics of 'Directions in hyperbolic lattices'. Together they form a unique fingerprint.

Cite this