1. CMB 2011 (vol 54 pp. 739)
|The Infimum in the Metric Mahler Measure|
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.
Keywords:Weil height, Mahler measure, metric Mahler measure, Lehmer's problem
2. CMB 2008 (vol 51 pp. 57)
|A Note on Integer Symmetric Matrices and Mahler's Measure |
We find a lower bound on the absolute value of the discriminant of the minimal polynomial of an integral symmetric matrix and apply this result to find a lower bound on Mahler's measure of related polynomials and to disprove a conjecture of D. Estes and R. Guralnick.
Keywords:integer matrices, Lehmer's problem, Mahler's measure