episciences.org_156_1669886724
1669886724
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
HardyRamanujan Journal
28047370
10.46298/journals/hrj
https://hrj.episciences.org
01
01
2007
Volume 30  2007
Carmichael number with three prime factors.
D R
HeathBrown
Let $C_3(x)$ be the number of Carmichael numbers $n\le x$ having exactly 3 prime factors. It has been conjectured that $C_3(x)$ is of order $x^{1/3}(\log x)^{1/3}$ exactly. We prove an upper bound of order $x^{7/20+\varepsilon}$, improving the previous best result due to Balasubramanian and Nagaraj, in which the exponent $7/20$ was replaced by $5/14$.
The proof combines various elementary estimates with an argument using Kloosterman fractions, which ultimately relies on a bound for the Ramanujan sum.
01
01
2007
156
https://hal.archivesouvertes.fr/hal01112050v1
10.46298/hrj.2007.156
https://hrj.episciences.org/156

https://hrj.episciences.org/156/pdf