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On effective equidistribution of expanding translates of certain orbits in the space of lattices

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Number Theory, Analysis and Geometry

Abstract

We prove an effective version of a result obtained earlier by Kleinbock and Weiss [KW] on equidistribution of expanding translates of orbits of horospherical subgroups in the space of lattices.

Mathematics Subject classification (2010): 37A17; 37A25

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Notes

  1. 1.

    In [KM2] the statement of Theorem 5.2 involved the sup norm instead of the Euclidean one, which resulted in a restriction for ρ to be not greater than 1 ∕ k; thus we chose to refer to [BKM] for the Euclidean norm version.

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Acknowledgements

The authors are grateful to the Fields Institute for Research in Mathematical Sciences (Toronto, Canada), where this project has commenced, and to the referee for useful remarks. The work of the first named author was supported in part by NSF Grants DMS-0239463 and DMS-0801064, and that of the second author by NSF Grants DMS-0244406 and DMS-0801195.

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Correspondence to D. Y. Kleinbock .

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In memory of Serge Lang

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Kleinbock, D.Y., Margulis, G.A. (2012). On effective equidistribution of expanding translates of certain orbits in the space of lattices. In: Goldfeld, D., Jorgenson, J., Jones, P., Ramakrishnan, D., Ribet, K., Tate, J. (eds) Number Theory, Analysis and Geometry. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1260-1_18

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