The author studies the numbers \(\mu (n):=\min \max \{ |\sum_{k=0}^{n-1}x^{k}|\), \(|\sum_{k=0}^{n-1}x^{kn}|\} \), where the \(\min \) is taken over all unit vectors in the complex plane. \(\mu (2)\) and \(\mu (3)\) have been determined already in another paper of the author [“Packings and mappings related to certain minmax problems”, not yet published], so here the case \(n\geq 4\) is considered. Unfortunately, the main result is not valid since there is an essential error in the last step of the proof of one of the propositions (2.2), as was acknowledged by the author in the meantime.
There is a further result which says that a certain polynomial with coefficients \(0\) and \(1\) derived from \(\mu (n)\) does not have zeros on the unit circle. This seems to be correct.