Anup B Dixit ; M Ram Murty - A localized Erdős-Kac theorem

hrj:7433 - Hardy-Ramanujan Journal, May 6, 2021, Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan - https://doi.org/10.46298/hrj.2021.7433
A localized Erdős-Kac theorem

Authors: Anup B Dixit ; M Ram Murty

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.


Volume: Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan
Published on: May 6, 2021
Submitted on: April 30, 2021
Keywords: prime divisors,Erdős-Kac theorem,central limit theorem,2010 Mathematics Subject Classification. 11N25, 11N64, 11K65, 60F05,[MATH]Mathematics [math]


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