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正整数随机集合的最小公倍数

数论 2013-12-16 v2

作者: Javier Cilleruelo , Juanjo Rué , Paulius Šarka , Ana Zumalacárregui

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摘要

我们研究随机子集 $A\subset \{1,\dots, n\}$ 元素的最小公倍数的典型行为。例如，我们证明对于几乎所有子集 $A\subset\{1,\dots,n\}$ ， $\text{lcm}\{a:\ a\in A\}=2^{n(1+o(1))}$ 。

关键词

最小公倍数随机集合正整数数论概率数论

引用

@article{arxiv.1112.3013,
  title  = {The least common multiple of random sets of positive integers},
  author = {Javier Cilleruelo and Juanjo Rué and Paulius Šarka and Ana Zumalacárregui},
  journal= {arXiv preprint arXiv:1112.3013},
  year   = {2013}
}

备注

11 pages. The manuscript has been rearranged. New results were included and some of the proofs improved