Student Number Theory Seminar

Tuesday, October 4, 2022 9:30 am - 9:30 am EDT (GMT -04:00)

Sourabh Das, Department of Pure Math, University of Waterloo

"On the Omega function"

For a natural number n, Ω(n) counts the total number of prime factors of n, honoring their 
For x ≥ 2, the summatory function of Ω has the following well-known formula:
L Ω(n) = x log log x + B₂x + O   )
for some constant B₂. In this talk, I will introduce the notion of h-free and h-full numbers and 
asymptotic formulas for the summatory function of Ω restricted to these numbers. This talk will 
a variety of ideas and results used in analytic number theory to study such summatory functions.

MC 5417