Equidistribution of primitive rational points on expanding horospheres
Dynamical Systems
2023-11-29 v2 Number Theory
Abstract
We confirm a conjecture of Jens Marklof regarding the equidistribution of certain sparse collections of points on expanding horospheres. These collections are obtained by intersecting the expanded horosphere with a certain manifold of complementary dimension and turns out to be of arithmetic nature. This equidistribution result is then used along the lines suggested by Marklof to give an analogue of a result of W. Schmidt regarding the distribution of shapes of lattices orthogonal to integer vectors.
Keywords
Cite
@article{arxiv.1305.2678,
title = {Equidistribution of primitive rational points on expanding horospheres},
author = {Manfred Einsiedler and Shahar Mozes and Nimish Shah and Uri Shapira},
journal= {arXiv preprint arXiv:1305.2678},
year = {2023}
}
Comments
Revised version. To appear in Compositio