Equidistribution of primitive rational points on expanding horospheres

Manfred Einsiedler, Shahar Mozes, Nimish Shah, Uri Shapira

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

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 languageAmerican English
Pages (from-to)667-692
Number of pages26
JournalCompositio Mathematica
Volume152
Issue number4
DOIs
StatePublished - 1 Apr 2016

Bibliographical note

Publisher Copyright:
© Foundation Compositio Mathematica 2015.

Keywords

  • Equidistribution
  • Homogeneous spaces
  • Shapes of orthogonal lattices

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