Thursday, November 16, 2017 1:30 pm
-
1:30 pm
EST (GMT -05:00)
Farzad Aryan, McGill University
"On an extension of the Landau-Gonek formula"
Let
$\rho$
be
zero
of
the
Riemann
zeta
function.
The
Landau-Gonek formula
asserts
that
$$
\sum_{0<
\Im(\rho)<
T}
n^{\rho}=
-\frac{T}{2\pi}\lambda(n)
+
O(n
\log 2nT
\log
3n).
\textbf{
(I)
}
$$
where
$\lambda(n)
=
\log
p$
if
$n
=
p^i$
and
$\lambda(n)
=
0$ otherwise.
Roughly
speaking,
the
formula
says
that
the
support
of the
above
sum
is
on
prime
numbers.
In
this
talk
we
will
discuss
a formula
similar
to
(I)
that
is
supported
on
the
product
of
two prime
numbers.
We
will
also
look
into
applications
of
these formulas.
MC 5501