Journal
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
Volume 2018, Issue 21, Pages 6581-6610Publisher
OXFORD UNIV PRESS
DOI: 10.1093/imrn/rnx081
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Funding
- European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013)/ERC Grant [291147]
- EPSRC [EP/K034383/1]
- EPSRC [EP/K034383/1] Funding Source: UKRI
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Einsiedler, Mozes, Shah, and Shapira [Compos. Math. 152 (2016), 667-92] 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 classification 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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