10.46298/hrj.2021.7433
https://hrj.episciences.org/7433
Dixit, Anup B
Anup B
Dixit
Ram Murty, M
M
Ram Murty
A localized Erdős-Kac theorem
Let ω_y (n) be the number of distinct prime divisors of n not exceeding y. If y_n is an increasing function of n such that log y_n = o(log n), we study the distribution of ω_{y_n} (n) and establish an analog of the Erdős-Kac theorem for this function. En route, we also prove a variant central limit theorem for random variables, which are not necessarily independent, but are well approximated by independent random variables.
episciences.org
prime divisors
Erdős-Kac theorem
central limit theorem
2010 Mathematics Subject Classification. 11N25, 11N64, 11K65, 60F05
[MATH]Mathematics [math]
2021-05-06
2021-05-06
2021-05-06
en
journal article
https://hal.archives-ouvertes.fr/hal-03208199v1
2804-7370
https://hrj.episciences.org/7433/pdf
VoR
application/pdf
Hardy-Ramanujan Journal
Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2020
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