ON THE QUESTION OF THE STRUCTURE OF THE SUBFIELD OF INVARIANTS OF A CYCLIC GROUP OF AUTOMORPHISMS OF THE FIELDQ(x1,...,xn)
V E Voskresenskiĭ · Mathematics of the USSR-Izvestiya · 1970
The subfield L of the field K = Q(x1,...,xn) consisting of invariant functions relative to a cyclic permutation of the indeterminates is interpreted as the field of rational functions on a certain torus defined over Q. On this basis, a necessary condition is derived for pure transcendence of L over Q from which are obtained a number of counterexamples. A list is also given of fields L which are purely transcendental over Q.