Additive energy and the metric Poissonian property
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 a1+a2=a3+a4 with ai∈A ) and the metric Poissonian property, which is a fine-scale equidistribution property for dilates of A modulo 1 . There appears to be reasonab...
| Hauptverfasser: | , , , |
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| Format: | Journal article |
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Cambridge University Press
2018
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| _version_ | 1826272987409547264 |
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| author | Bloom, T Chow, S Gafni, A Walker, A |
| author_facet | Bloom, T Chow, S Gafni, A Walker, A |
| author_sort | Bloom, T |
| collection | OXFORD |
| description | 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 a1+a2=a3+a4 with ai∈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 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. |
| first_indexed | 2024-03-06T22:21:14Z |
| format | Journal article |
| id | oxford-uuid:552104fe-82db-4846-82b8-9ad9daf6cec5 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T22:21:14Z |
| publishDate | 2018 |
| publisher | Cambridge University Press |
| record_format | dspace |
| spelling | oxford-uuid:552104fe-82db-4846-82b8-9ad9daf6cec52022-03-26T16:42:07ZAdditive energy and the metric Poissonian propertyJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:552104fe-82db-4846-82b8-9ad9daf6cec5Symplectic Elements at OxfordCambridge University Press2018Bloom, TChow, SGafni, AWalker, ALet 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 a1+a2=a3+a4 with ai∈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 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. |
| spellingShingle | Bloom, T Chow, S Gafni, A Walker, A Additive energy and the metric Poissonian property |
| title | Additive energy and the metric Poissonian property |
| title_full | Additive energy and the metric Poissonian property |
| title_fullStr | Additive energy and the metric Poissonian property |
| title_full_unstemmed | Additive energy and the metric Poissonian property |
| title_short | Additive energy and the metric Poissonian property |
| title_sort | additive energy and the metric poissonian property |
| work_keys_str_mv | AT bloomt additiveenergyandthemetricpoissonianproperty AT chows additiveenergyandthemetricpoissonianproperty AT gafnia additiveenergyandthemetricpoissonianproperty AT walkera additiveenergyandthemetricpoissonianproperty |