Equidistribution of primitive rational points on expanding horospheres

Manfred Einsiedler; Shahar Mozes; Nimish Shah; Uri Shapira

doi:10.1112/S0010437X15007605

Equidistribution of primitive rational points on expanding horospheres

Manfred Einsiedler, Shahar Mozes, Nimish Shah, Uri Shapira

The Hebrew University of Jerusalem, Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

We confirm a conjecture of Marklof regarding the limiting distribution 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 result is then used along the lines suggested by Marklof to give an analogue of a result of Schmidt regarding the distribution of shapes of lattices orthogonal to integer vectors.

Original language	English
Pages (from-to)	667-692
Number of pages	26
Journal	Compositio Mathematica
Volume	152
Issue number	4
DOIs	https://doi.org/10.1112/S0010437X15007605
State	Published - 1 Apr 2016

Keywords

Equidistribution
Homogeneous spaces
Shapes of orthogonal lattices

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1112/S0010437X15007605

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N2 - We confirm a conjecture of Marklof regarding the limiting distribution 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 result is then used along the lines suggested by Marklof to give an analogue of a result of Schmidt regarding the distribution of shapes of lattices orthogonal to integer vectors.

AB - We confirm a conjecture of Marklof regarding the limiting distribution 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 result is then used along the lines suggested by Marklof to give an analogue of a result of Schmidt regarding the distribution of shapes of lattices orthogonal to integer vectors.

KW - Equidistribution

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KW - Shapes of orthogonal lattices

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Equidistribution of primitive rational points on expanding horospheres

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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