EXTREMAL MAHLER MEASURES AND Ls NORMS OF POLYNOMIALS RELATED TO BARKER SEQUENCES.

In the present paper, we study the class LPn which consists of Laurent polynomials ... with all coefficients ck equal to -1 or 1. Such polynomials arise in the study of Barker sequences of even length -- binary sequences with minimal possible autocorrelations. By using an elementary (but not trivial) analytic argument, we prove that polynomials Rn(z) with all coefficients ck = 1 have minimal Mahler measures in the class LPn. In conjunction with an estimate M(Rn) > n - 2/πlogn + O(1) proved in an earlier paper, we deduce that polynomials whose coefficients form a Barker sequence would possess unlikely large Mahler measures. A generalization of this result to Ls norms is also given. [ABSTRACT FROM AUTHOR]