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arXiv · 1305.2678

Equidistribution of primitive rational points on expanding horospheres

Manfred Einsiedler·Shahar Mozes·Nimish Shah·Uri Shapira
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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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Manfred Einsiedler, Shahar Mozes, Nimish Shah, Uri Shapira. 2013-05-13. Equidistribution of primitive rational points on expanding horospheres. https://doi.org/10.1112/s0010437x15007605

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