A. Dubickas and C. Smyth introduced the metric Mahler measure
where M(α) denotes the usual (logarithmic) Mahler measure of . This definition extends in a natural way to the t-metric Mahler measure by replacing the sum with the usual Lt norm of the vector (M(α1),…,M(αN)) for any t≧1. For α∊ℚ, we prove that the infimum in Mt(α) may be attained using only rational points, establishing an earlier conjecture of the second author. We show that the natural analogue of this result fails for general by giving an infinite family of quadratic counterexamples. As part of this construction, we provide an explicit formula to compute Mt(D1/k) for a squarefree D∊ℕ.
 Borwein, P.Dobrowolski, E.Mossinghoff, M. J.2007Lehmer's problem for polynomials with odd coefficientsAnn. of Math.166347–366.