10.46298/hrj.2007.156
https://hrj.episciences.org/156
Heath-Brown , D R
D R
Heath-Brown
Carmichael number with three prime factors.
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.
episciences.org
Upper bound
Three prime factors
Carmichael numbers
Ramanujan sum
[MATH] Mathematics [math]
2015-06-12
2007-01-01
2007-01-01
en
journal article
https://hal.archives-ouvertes.fr/hal-01112050v1
2804-7370
https://hrj.episciences.org/156/pdf
VoR
application/pdf
Hardy-Ramanujan Journal
Volume 30 - 2007
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