Hardy Ramanujan Journal |

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.

Source : oai:HAL:hal-03208199v1

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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