中文

短区间内平方满数的方差 II

数论 2023-11-23 v1

摘要

在本文中,我们继续研究短区间(x,x+2xH+H2](x, x + 2 \sqrt{x} H + H^2](其中Xx2XX \le x \le 2X)内平方满数个数的方差。我们在无条件情形下对范围XϵHX0.180688...X^\epsilon \le H \le X^{0.180688...}内、以及在Riemann假设或Lindel"{o}f假设条件下对最优范围XϵHX0.25ϵX^\epsilon \le H \le X^{0.25 - \epsilon}内的该方差得到了期望的渐近式。

关键词

引用

@article{arxiv.2311.13463,
  title  = {Variance of squarefull numbers in short intervals II},
  author = {Tsz Ho Chan},
  journal= {arXiv preprint arXiv:2311.13463},
  year   = {2023}
}

备注

17 pages, welcome any comments. arXiv admin note: text overlap with arXiv:2205.12108