Student Number Theory SeminarExport this event to calendar

Tuesday, October 4, 2022 — 9:30 AM EDT

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

MC 5417

https://uwaterloo.zoom.us/j/94981169066?pwd=d2M1SE1qV3VCRk14WlRUaDI5WTdJZz09

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