Limiting distributions of translates of divergent diagonal orbits

Uri Shapira, Cheng Zheng

Research output: Contribution to journalArticlepeer-review


We define a natural topology on the collection of (equivalence classes up to scaling of) locally finite measures on a homogeneous space and prove that in this topology, pushforwards of certain infinite-volume orbits equidistribute in the ambient space. As an application of our results we prove an asymptotic formula for the number of integral points in a ball on some varieties as the radius goes to infinity.

Original languageEnglish
Pages (from-to)1747-1793
Number of pages47
JournalCompositio Mathematica
Issue number9
StatePublished - 1 Sep 2019


  • Ratner's theorem
  • convex polytopes
  • counting lattice points
  • homogeneous spaces
  • homothety classes of locally finite measures
  • translates of divergent orbits

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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