Monday, May 13, 2013 11:30 am
-
11:30 am
EDT (GMT -04:00)
Blake Madill, Pure Mathematics, University of Waterloo
"Small Salem Numbers"
A
great
deal
is
known
about
the
Pisot-Vijayaraghavan
(P.V.)
numbers.
However,
less
is
known
about
the
set
of
Salem
numbers.
The
main
result
in
this
area,
due
to
Salem,
is
that
each
P.V.
number
is
a
limit
point
of
the
set
of
Salem
numbers.
The
smallest
known
P.V.
number
is
approximately
$\theta_0=1.3247$.
Any
interval
$(0,a)$,
$a\geq\theta_0,$
contains
infinitely
many
Salem
numbers.
Therefore
it
is
reasonable
to
be
interested
in
small
Salem
numbers.
We
present
all
relevant
definitions
and
discuss
results
by
Boyd,
which
allow
one
to
find
Salem
numbers
from
given
P.V.
numbers.