期刊
MATHEMATIKA
卷 65, 期 4, 页码 929-949出版社
LONDON MATH SOC
DOI: 10.1112/S002557931900024X
关键词
-
资金
- Austrian Science Fund (FWF) [Y-901, F 5512-N26]
- FWF [Y-901]
- FWF project [W1230]
- EPSRC Programme Grant [EP/J018260/1]
- EPSRC [EP/J018260/1] Funding Source: UKRI
We consider sequences of the form (a(n)alpha)(n) mod 1, where alpha is an element of [0, 1] and where (a(n))(n) is a strictly increasing sequence of positive integers. If the asymptotic distribution of the pair correlations of this sequence follows the Poissonian model for almost all alpha in the sense of Lebesgue measure, we say that (a(n))(n) has the metric pair correlation property. Recent research has revealed a connection between the metric theory of pair correlations of such sequences, and the additive energy of truncations of (a(n))(n). Bloom, Chow, Gafni and Walker speculated that there might be a convergence/divergence criterion which fully characterizes the metric pair correlation property in terms of the additive energy, similar to Khintchine's criterion in the metric theory of Diophantine approximation In the present paper we give a negative answer to such speculations, by showing that such a criterion does not exist. To this end, we construct a sequence (a(n))(n) having large additive energy which, however, maintains the metric pair correlation property.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据