English

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