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
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