Equidistribution of elements of norm 1 in cyclic extensions

Abstract

Upon quotienting by units, the elements of norm 1 in a number field K form a countable subset of a torus of dimension r1 + r2 - 1 where r1 and r2 are the numbers of real and pairs of complex embeddings. When K is Galois with cyclic Galois group we demonstrate that this countable set is equidistributed in this torus with respect to a natural partial ordering.