期刊
MATHEMATIKA
卷 64, 期 3, 页码 679-700出版社
LONDON MATH SOC
DOI: 10.1112/S0025579318000207
关键词
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资金
- National Science Foundation [DMS-1440140]
- EPSRC [EP/J018260/1, EP/M50659X/1]
- EPSRC [EP/J018260/1] Funding Source: UKRI
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 alpha(1) + alpha(2) = a(3) + a(4) with a(i) is an element of 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.
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