Abstract Let ( f n ) n = 1 ∞ be a sequence of polynomials and α > 1 . In this paper we study the distribution of the sequence ( f n ( α ) ) n = 1 ∞ modulo one. We give sufficient conditions for a sequence ( f n ) n = 1 ∞ to ensure that for Lebesgue almost every α > 1 the sequence ( f n ( α ) ) n = 1 ∞ has Poissonian pair correlations. In particular, this result implies that for Lebesgue almost every α > 1 , for any k ≥ 2 the sequence ( α n k ) n = 1 ∞ has Poissonian pair correlations.

中文翻译：

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多项式序列的等分布结果

摘要 令 ( fn ) n = 1 ∞ 为多项式序列且 α > 1 。在本文中，我们研究序列 ( fn ( α ) ) n = 1 ∞ 模 1 的分布。我们给出了序列 ( fn ) n = 1 ∞ 的充分条件，以确保对于 Lebesgue 几乎每个 α > 1 序列 ( fn ( α ) ) n = 1 ∞ 都具有泊松对相关性。特别地，这个结果意味着对于 Lebesgue 几乎每个 α > 1 ，对于任何 k ≥ 2 序列 ( α nk ) n = 1 ∞ 都具有泊松对相关性。