Bloom, Thomas F., Chow, Samuel Khai Ho, Gafni, Ayla et al. (1 more author) (2018) Additive energy and the metric Poissonian property. Mathematika. pp. 679-700. ISSN 2041-7942
Abstract
Let $A$ be a set of natural numbers. Recent work has suggested a strong link between the additive energy of $A$ (the number of solutions to $a_1 + a_2 = a_3 + a_4$ with $a_i \in A$) and the metric Poissonian property, which is a fine-scale equidistribution property for dilates of $A$ modulo $1$. There appears to be reasonable evidence to speculate a sharp Khintchine-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.
Metadata
Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 University College London. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details |
Keywords: | pair correlations, distribution modulo 1, metric diophantine approximation, additive combinatorics, large deviations |
Dates: |
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Institution: | The University of York |
Academic Units: | The University of York > Faculty of Sciences (York) > Mathematics (York) |
Depositing User: | Pure (York) |
Date Deposited: | 26 Feb 2018 10:00 |
Last Modified: | 06 Dec 2023 12:20 |
Published Version: | https://doi.org/10.1112/S0025579318000207 |
Status: | Published |
Refereed: | Yes |
Identification Number: | https://doi.org/10.1112/S0025579318000207 |
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