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Effective equidistribution of rational points on expanding horospheres

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Original languageEnglish
Article numberrnx081
Pages (from-to)6581–6610
Number of pages30
JournalInternational Mathematics Research Notices
Volume2018
Issue number21
Early online date29 Apr 2017
DOIs
DateAccepted/In press - 22 Mar 2017
DateE-pub ahead of print - 29 Apr 2017
DatePublished (current) - Nov 2018

Abstract

Einsiedler, Mozes, Shah and Shapira [Compos. Math. 152 (2016), 667-692] prove an equidistribution theorem for rational points on expanding horospheres in the space of d-dimensional Euclidean lattices, with d 3. Their proof exploits measure classication results, but provides no insight into the rate of convergence. We pursue here an alternative approach, based on harmonic analysis and Weil's bound for Kloosterman sums, which in dimension d = 3 yields an effective estimate on the rate of convergence.

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  • Full-text PDF (accepted author manuscript)

    Rights statement: This is the author accepted manuscript (AAM). The final published version (version of record) is available online via OUP at https://academic.oup.com/imrn/article/3782827/Effective-Equidistribution-of-Rational-Points-on?searchresult=1#80675421. Please refer to any applicable terms of use of the publisher.

    Accepted author manuscript, 396 KB, PDF document

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