Number Theory seminar

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.