中文

Erdős-Hooley Delta 函数均值的一个上界

数论 2023-12-11 v4

摘要

Erdős-Hooley Delta 函数对 nNn\in\mathbb{N} 定义为 Δ(n)=supuR#{dn:eu<deu+1}\Delta(n)=\sup_{u\in\mathbb{R}} \#\{d|n : e^u<d\le e^{u+1}\}。我们证明对所有 x100x\ge100nxΔ(n)x(loglogx)11/4\sum_{n\le x} \Delta(n) \ll x(\log\log x)^{11/4}。这改进了 Hooley、Hall--Tenenbaum 以及 La Bret\`eche-Tenenbaum 的早期工作。

关键词

引用

@article{arxiv.2306.08615,
  title  = {An upper bound on the mean value of the Erd\H{o}s-Hooley Delta function},
  author = {Dimitris Koukoulopoulos and Terence Tao},
  journal= {arXiv preprint arXiv:2306.08615},
  year   = {2023}
}

备注

18 pages. Some minor changes. This is the final version that will apper in Proc. London Math. Soc