Equidistribution of primitive rational points on expanding horospheres

Manfred Einsiedler, Shahar Mozes, Nimish A. Shah, Uri Shapira

Type: Article

Publication Date: 2015-11-09

Citations: 24

DOI: https://doi.org/10.1112/s0010437x15007605

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.

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arXiv (Cornell University) - View - PDF
Repository for Publications and Research Data (ETH Zurich) - View - PDF
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Compositio Mathematica - View - PDF

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