当前位置: X-MOL 学术Bull. Aust. Math. Soc. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
A CONDITIONAL DENSITY FOR CARMICHAEL NUMBERS
Bulletin of the Australian Mathematical Society ( IF 0.6 ) Pub Date : 2020-02-13 , DOI: 10.1017/s000497271900145x
THOMAS WRIGHT

Under sufficiently strong assumptions about the first prime in an arithmetic progression, we prove that the number of Carmichael numbers up to$X$is$\gg X^{1-R}$, where$R=(2+o(1))\log \log \log \log X/\text{log}\log \log X$. This is close to Pomerance’s conjectured density of$X^{1-R}$with$R=(1+o(1))\log \log \log X/\text{log}\log X$.

中文翻译:

卡迈克尔数的条件密度

在关于算术级数中的第一个素数的足够强的假设下,我们证明了卡迈克尔数的数量高达$X$$\gg X^{1-R}$, 在哪里$R=(2+o(1))\log \log \log \log X/\text{log}\log \log X$. 这接近 Pomerance 的猜想密度$X^{1-R}$$R=(1+o(1))\log \log \log X/\text{log}\log X$.
更新日期:2020-02-13
down
wechat
bug