Additive energy and the metric Poissonian property
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Peer-reviewed
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Abstract
Let
- a_4$ 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 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.
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Keywords
math.NT, math.NT, math.CO, 11J71, 11J83, 05B10, 11B30, 60F10
Journal Title
Mathematika
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Journal ISSN
0025-5793
2041-7942
2041-7942
Volume Title
64
Publisher
Wiley
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All rights reserved