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.
| Original language | English |
|---|---|
| Pages (from-to) | 161-186 |
| Number of pages | 26 |
| Journal | Journal für die reine und angewandte Mathematik |
| Volume | 2018 |
| Issue number | 740 |
| Early online date | 17 Dec 2015 |
| DOIs | |
| Publication status | Published - Jul 2018 |
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Dive into the research topics of 'Directions in hyperbolic lattices'. Together they form a unique fingerprint.Profiles
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Professor Jens Marklof
- School of Mathematics - Henry Overton Wills Professor of Mathematics
- Probability, Analysis and Dynamics
- Pure Mathematics
- Ergodic theory and dynamical systems
Person: Academic , Member
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