拟随机算术置换
Quasirandom Arithmetic Permutations
摘要：
以前，作者介绍了准随机排列，排列的$\mathbb{Z}_n$映射区间集与低差异。在这里，我们表明，几个自然数理论的排列是准随机的，一些非常强烈的。拟随机性是通过离散的傅里叶分析和Erdos-Turan不等式，以及通过其他手段建立的。我们应用我们的结果在Sos排列取得进展的一些问题有关的序列的分数部分的倍数的不合理。在整个讨论中提出了几个有趣的新的开放问题。
英文摘要：
Previously, the author introduced quasirandom permutations, permutations of $\mathbb{Z}_n$ which map intervals to sets with low discrepancy. Here we show that several natural number-theoretic permutations are quasirandom, some very strongly so. Quasirandomness is established via discrete Fourier analysis and the Erdos-Turan inequality, as well as by other means. We apply our results on Sos permutations to make progress on a number of questions relating to the sequence of fractional parts of multiples of an irrational. Several intriguing new open problems are presented throughout the discussion.
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