Equidistribution of Elements of Norm 1 in Cyclic Extensions
MFO Scientific ProgramResearch in Pairs 2013
Petersen, Kathleen L.
Sinclair, Christopher D.
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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 $r_1$ 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.