Equidistribution of elements of norm 1 in cyclic extensions

Kathleen L. Petersen; Christopher D. Sinclair

doi:10.5486/PMD.2023.9553

Equidistribution of elements of norm 1 in cyclic extensions

Kathleen L. Petersen, Christopher D. Sinclair

Research output: Contribution to journal › Article › peer-review

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 a finite cover of this torus with respect to a natural partial ordering induced by Hilbert s Theorem 90.

Original language	English (US)
Pages (from-to)	215-223
Number of pages	9
Journal	Publicationes Mathematicae Debrecen
Volume	103
Issue number	1-2
DOIs	https://doi.org/10.5486/PMD.2023.9553
State	Published - 2023
Externally published	Yes

Bibliographical note

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© 2023 University of Debrecen, Institute of Mathematics. All rights reserved.

Keywords

Key words and phrases: equidistribution, cyclic number field, Hecke zeta function, norm 1.

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Equidistribution of elements of norm 1 in cyclic extensions

Abstract

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