An extremal problem for polynomials

We give a solution to an extremal problem for polynomials, which asks for complex numbers alpha(0),..., alpha(n) of unit magnitude that minimise the largest supremum norm on the unit circle for all polynomials of degree n whose k-th coefficient is either alpha(k) or -alpha(k). (C) 2013 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.