Canad. Math. Bull. 54(2011), 739-747
Printed: Dec 2011
Dubickas and Smyth defined the metric Mahler measure on the
multiplicative group of non-zero algebraic numbers.
The definition involves taking an infimum over representations
of an algebraic number $\alpha$ by other
algebraic numbers. We verify their conjecture that the
infimum in its definition is always achieved, and we establish its
analog for the ultrametric Mahler measure.
Weil height, Mahler measure, metric Mahler measure, Lehmer's problem
11R04 - Algebraic numbers; rings of algebraic integers
11R09 - Polynomials (irreducibility, etc.)