Number Theory Seminar: The parametrized family of metric Mahler measures

  • Date: 01/21/2010
Charles Samuels (PIMS/SFU/UBC)

University of British Columbia


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.


3:0pm-3:50pm, WMAX 110

Refreshments will be served at 3:50pm