Effective equidistribution of rational points on expanding horospheres

Min Lee; Jens Marklof

doi:10.1093/imrn/rnx081

Effective equidistribution of rational points on expanding horospheres

Min Lee, Jens Marklof

Research output: Contribution to journal › Article (Academic Journal) › peer-review

6 Citations (Scopus)

331 Downloads (Pure)

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.

Original language	English
Article number	rnx081
Pages (from-to)	6581–6610
Number of pages	30
Journal	International Mathematics Research Notices
Volume	2018
Issue number	21
Early online date	29 Apr 2017
DOIs	https://doi.org/10.1093/imrn/rnx081
Publication status	Published - 1 Nov 2018

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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.
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Effective joint equidistribution of primitive rational points on expanding horospheres
Lee, M., El-Baz, D. & Huang, B., 12 Apr 2021, (Accepted/In press) In: Journal of the European Mathematical Society. 21 p.
Research output: Contribution to journal › Article (Academic Journal) › peer-review

Open Access

Dr Min Lee
- min.leebristol.acuk
- School of Mathematics - Senior Lecturer
- Pure Mathematics
Person: Academic , Member

Cite this

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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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Effective equidistribution of rational points on expanding horospheres

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Effective joint equidistribution of primitive rational points on expanding horospheres

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Dr Min Lee

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