## Number Theory Seminar: The parametrized family of metric Mahler measures

- Date: 01/21/2010

Lecturer(s):
Charles Samuels (PIMS/SFU/UBC)

Location:

University of British Columbia

Description:

Let $M(\alpha)$ denote the Mahler measure of the algebraic

number $\alpha$. Dubickas and Smyth constructed a modified version

$M_1$ of $M$ having the triangle inequality. $M_1$ is called the metric

Mahler measure. We produce an entire parametrized family $\{M_t\}$ of

metric Mahler measures which gives rise to a new reformulation of

Lehmer's problem. We further examine the functions $t\mapsto

M_t(\alpha)$, for fixed $\alpha$, showing that they are constructed

piecewise from certain simpler functions.

Schedule: