Number Theory Seminar: Charles Samuels (PIMS/SFU/UBC)

Let x be an algebraic number and let M(x) denote its Mahler measure. If x = x1...xN the t-metric Mahler measure Mt(x) is a convenient way to study the smallest possible values of M(xn) in terms of x. In joint work with J. Jankauskas, we resolve an earlier conjecture regarding Mt(x) for rational x. This result suggests a generalization to higher degree x, which turns out, however, to be false. We provide an infinite family of quadratic counterexamples and discuss how the conjecture should be modified.