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Limiting distributions of translates of divergent diagonal orbits

Published online by Cambridge University Press:  02 August 2019

Uri Shapira
Affiliation:
Department of Mathematics, Technion, Haifa, Israel email ushapira@technion.ac.il
Cheng Zheng
Affiliation:
Department of Mathematics, Technion, Haifa, Israel email cheng.zheng@campus.technion.ac.il

Abstract

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.

Type
Research Article
Copyright
© The Authors 2019 

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Footnotes

The authors acknowledge the support of ISF grants 871/17, 662/15 and 357/13. The second author is in part supported at the Technion by a Fine Fellowship. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 754475).

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