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Equidistribution of primitive rational points on expanding horospheres

Published online by Cambridge University Press:  09 November 2015

Manfred Einsiedler ,
Shahar Mozes ,
Nimish Shah  and
Uri Shapira
Manfred Einsiedler
Affiliation:
ETH Zürich, CH-8092 Zürich, Switzerland email manfred.einsiedler@math.ethz.ch
Shahar Mozes
Affiliation:
Institute of Mathematics, The Hebrew University of Jerusalem, Givaat Ram, 91904 Jerusalem, Israel email mozes@math.huji.ac.il
Nimish Shah
Affiliation:
Ohio State University, Columbus 43210-1174, USA email shah@math.osu.edu
Uri Shapira
Affiliation:
Technion - Israel Institute of Technology, 32000 Haifa, Israel email ushapira@tx.technion.ac.il
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Abstract

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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.

Keywords

equidistributionhomogeneous spacesshapes of orthogonal lattices
Type
Research Article
Information
Compositio Mathematica , Volume 152 , Issue 4 , April 2016 , pp. 667 - 692
Copyright
© The Authors 2015 

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