Matilde Lalin, Université de Montréal
"Mahler measure of some K3-surfaces"
We
study
the
Mahler
measure
of
the
three-variable
Laurent
polynomial
x+1/x+y+1/y+z-k
where
k
is
a
parameter.
The
zeros
of
this
polynomial
define
(after
desingularization)
a
family
K3-surfaces.
In
favorable
cases,
a
singular
K3-surface
is
obtained
and
the
Mahler
measure
is
related
to
its
L-function.
This
was
first
studied
by
Marie-Jose
Bertin.
In
this
talk
we
present
some
new
formulas.
This
is
joint
work
with
Marie-Jose
Berin,
Amy
Feaver,
Jenny
Fuselier,
and
Michelle
Manes.