Joint Pure Math and Computational Mathematics Colloquium
Monday, May 16th
DC 1302 - Refreshments at 3:30pm, Talk at 4:00pm
Yuri V. Matiyasevich St.Petersburg Department of V. A. Steklov Institute of Mathematics, Russia
"Computer experiments for approximating Riemann's zeta function by finite Dirichlet series"
In
2011
the
speaker
began
to
work
with
nite
Dirichlet
series
of
length
N
vanishing
at
N1
initial
non-trivial
zeroes
of
Riemann's
zeta
function.
Intensive
multiprecision
calculations
revealed
several
interesting
phenom-
ena.
First,
such
series
approximate
with
great
accuracy
the
values
of
the
product
(1
2
2
s)(s)
for
a
large
range
of
s
lying
inside
the
critical
strip
and
to
the
left
of
it
(even
better
approximations
can
be
obtained
by
dealing
with
ratios
of
certain
finite
Dirichlet
series).
In
particular
the
series
vanish
also
very
close
to
many
other
non-trivial
zeroes
of
the
zeta
function
(initial
non-trivial
zeroes
\know
about"
subsequent
non-trivial
zeroes).
Second,
the
coecients
of
such
series
encode
prime
numbers
in
several
ways.
So
far
no
theoretical
explanation
was
given
to
the
observed
phenom-
ena.
The
ongoing
research
can
be
followed
at
http://logic.pdmi.ras.ru/~yumat/personaljournal/finitedirichlet