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A metric theory of minimal gaps. (arXiv:1710.01911v1 [math.NT])
来源于:arXiv
We study the minimal gap statistic for fractional parts of sequences of the
form $\mathcal A^\alpha = \{\alpha a(n)\}$ where $\mathcal A = \{a(n)\}$ is a
sequence of distinct of integers. Assuming that the additive energy of the
sequence is close to its minimal possible value, we show that for almost all
$\alpha$, the minimal gap $\delta_{\min}^\alpha(N)=\min\{\alpha a(m)-\alpha
a(n)\bmod 1: 1\leq m\neq n\leq N\}$ is close to that of a random sequence. 查看全文>>