A note on the Hasse norm principle

Author:

Koymans Peter1,Rome Nick2ORCID

Affiliation:

1. Institute for Theoretical Studies ETH Zurich Zurich Switzerland

2. Insititue of Analysis and Number Theory Graz University of Technology Graz Austria

Abstract

AbstractLet be a finite, abelian group. We show that the density of ‐extensions satisfying the Hasse norm principle exists, when the extensions are ordered by discriminant. This strengthens earlier work of Frei–Loughran–Newton, who obtained a density result under the additional assumption that is cyclic with denoting the smallest prime divisor of .

Funder

ETH Zürich Foundation

Publisher

Wiley

Subject

General Mathematics

Reference10 articles.

1. J. W. S.CasselsandA.Fröhlich Algebraic number theory Proceedings of an instructional conference organized by the London Math. Soc. (a NATO Advanced Study Institute) with the support of the International Mathematical Union Academic Press London Thompson Book Co. Inc. Washington DC 1967.

2. The Hasse norm principle for abelian extensions

3. Number fields with prescribed norms (with an appendix by Yonatan Harpaz and Olivier Wittenberg)

4. ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group

5. P.KoymansandN.Rome Weak approximation on the norm one torus arXiv:2211.05911.

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