论文标题
序列$ \ {α\ sqrt {n} \} $的间隙统计
Gap Statistics of the Sequence $\{α\sqrt{n}\}$
论文作者
论文摘要
Elkies-McMullen（2004）显示了序列$ \ {\ sqrt {n} \} $中的差距，以具有限制分布，而不是指数分布。但是，猜想是序列$ \ {α\ sqrt {n} \} $中间隙的分布是指数的，前提是$α^2 $是不合理的。对于几乎所有$α$的值，我们证明了朝这个方向迈出的重要一步。特别是，我们表明所有相关性都是沿着子序列的泊松人。因此，我们的结果意味着GAP分布沿着相同的子序列收敛到指数分布。
The gaps in the sequence $\{\sqrt{n}\}$ were shown by Elkies-McMullen (2004) to have a limiting distribution which is not the exponential distribution. However it is conjectured that the distribution of gaps in the sequence $\{α\sqrt{n}\}$ is exponential, provided $α^2$ is irrational. For almost all values of $α$, we prove an important step in this direction. In particular, we show that all the correlations are Poissonian along a subsequence. Therefore, our result implies that the gap distribution converges to the exponential distribution along the same subsequence.
