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SUMMARY:Ertan Elma (Mathematics Research Center-Azerbaijan State Oil and I
 ndustry University)
DTSTART:20251119T150000Z
DTEND:20251119T160000Z
DTSTAMP:20260422T104903Z
UID:FGC-IPM/60
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FGC-IPM/60/"
 >Number of prime factors with a given multiplicity</a>\nby Ertan Elma (Mat
 hematics Research Center-Azerbaijan State Oil and Industry University) as 
 part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nFor natural numb
 ers $k\, n \\ge 1$\, let $\\omega_k(n)$ be the number of prime factors of 
 $n$ with multiplicity $k$. The functions $\\omega_k(n)$ with $k \\ge 1$ ar
 e refined versions of the well-known function $\\omega(n)$ counting the nu
 mber of distinct prime factors of $n$ without any conditions on the multip
 licities. In this talk\, we will cover several elementary\, analytic and p
 robabilistic results about the functions $\\omega_k(n)$ with $k \\ge 1$ an
 d their function field analogues in polynomial rings with coefficients fro
 m a finite field. In particular\, we will see that the function $\\omega_1
 (n)$ and its function field analogue satisfy the Erd\\H{o}s--Kac Theorem. 
 The results we will see in this talk are based on joint works with Yu-Ru L
 iu\, with Sourabhashis Das\, Wentang Kuo and Yu-Ru Liu\, and with Greg Mar
 tin.\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/60/
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