Effective equidistribution of rational points on expanding horospheres

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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.
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
Publication statusPublished - 1 Nov 2018

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