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Search: All articles in the CMB digital archive with keyword Lehmer's problem

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1. CMB 2011 (vol 54 pp. 739)

Samuels, Charles L.
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
Categories:11R04, 11R09

2. CMB 2008 (vol 51 pp. 57)

Dobrowolski, Edward
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
Categories:11C20, 11R06

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