Equidistribution of Elements of Norm 1 in Cyclic Extensions

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 counta...

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Bibliographic Details
Published in:arXiv.org 2022-11
Main Authors: Petersen, Kathleen L, Sinclair, Christopher D
Format: Article
Language:English
Subjects:
Number theory
Toruses
Online Access:Get full text
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Summary: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.
ISSN:2331-8422