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

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In a previous paper [1] we proved that [Display omitted] when n + 1 is prime. In this paper we prove that [Display omitted] when n − 1 is a prime power, and [Display omitted] when n ⩾ 3 is a prime power. We give explicit constructions of n-tuples ( z 1,..... z n ) 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