Equidistribution of Elements of Norm 1 in Cyclic Extensions

Kathleen L. Petersen; Christopher D. Sinclair

paper

Equidistribution of Elements of Norm 1 in Cyclic Extensions

arXiv:1404.4648

Abstract

Upon quotienting by units, the elements of norm 1 in a number field $K$ form a countable subset of a torus of dimension $r_{1} + r_{2} - 1$ where $r_{1}$ and $r_{2}$ 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 a finite cover of this torus with respect to a natural partial ordering induced by Hilbert's Theorem 90.

7 pages