Sums of monomials with large Mahler measure

For n >= 1 let A(n) := {P : P(z) = Sigma(n)(j=1)z(kj) : 0 <= k(1) < k(2) < ... < k(n), k(j) is an element of Z}, that is, A(n) is the collection of all sums of n distinct monomials. These polynomials are also called Newman polynomials. If alpha < beta are real numbers then the Mahler measure M-0(Q, [alpha, beta]) is defined for bounded measurable functions Q(e(it)) on [alpha, beta] as M-0(Q, [alpha, beta]) := exp (1/beta - alpha integral(beta)(alpha) log vertical bar Q(e(it))vertical bar dt). Let I := [alpha, beta]. In this paper we examine the quantities L-n(0)(I) := sup M-P is an element of An(0)(P, I)/root n and L-0(I) := lim(n ->infinity) inf L-n(0) (I) with 0 < vertical bar I vertical bar := beta - alpha <= 2 pi. (C) 2014 Elsevier Inc. All rights reserved.