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Additive energy and the metric Poissonian property
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Bloom, Thomas, Chow, Sam, Gafni, Ayla and Walker, Aled (2018) Additive energy and the metric Poissonian property. Mathematika, 64 (3). pp. 679-700. doi:10.1112/S0025579318000207 ISSN 0025-5793.
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Official URL: https://doi.org/10.1112/S0025579318000207
Abstract
Let be a set of natural numbers. Recent work has suggested a strong link between the additive energy of (the number of solutions to with ) and the metric Poissonian property, which is a fine-scale equidistribution property for dilates of modulo . There appears to be reasonable evidence to speculate a sharp Khinchin-type threshold, that is, to speculate that the metric Poissonian property should be completely determined by whether or not a certain sum of additive energies is convergent or divergent. In this article, we primarily address the convergence theory, in other words the extent to which having a low additive energy forces a set to be metric Poissonian.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Journal or Publication Title: | Mathematika | ||||||
Publisher: | London Mathematical Society | ||||||
ISSN: | 0025-5793 | ||||||
Official Date: | 19 June 2018 | ||||||
Dates: |
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Volume: | 64 | ||||||
Number: | 3 | ||||||
Page Range: | pp. 679-700 | ||||||
DOI: | 10.1112/S0025579318000207 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Copyright Holders: | © University College London 2018 | ||||||
Date of first compliant deposit: | 18 September 2019 | ||||||
Related URLs: | |||||||
Open Access Version: |
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