Explicit solutions to certain inf max problems from Turán power sum theory

In a previous paper [1] we proved that Figure optionsDownload full-size imageDownload as PowerPoint slide when n + 1 is prime. In this paper we prove that Figure optionsDownload full-size imageDownload as PowerPoint slide when n − 1 is a prime power, and Figure optionsDownload full-size imageDownload as PowerPoint slide when n ⩾ 3 is a prime power. We give explicit constructions of n-tuples (z1,..... zn) which we prove are global minima for these problems. These are two of the few times in Turán power sum theory where solutions in the inf max problem can be explicitly calculated.072006