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The Hasse norm principle for abelian extensions

Frei, C., Loughran, D. and Newton, R. (2018) The Hasse norm principle for abelian extensions. American Journal of Mathematics, 140 (6). pp. 1639-1685. ISSN 1080-6377

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To link to this item DOI: 10.1353/ajm.2018.0048

Abstract/Summary

We study the distribution of abelian extensions of bounded discriminant of a number field k which fail the Hasse norm principle. For example, we classify those finite abelian groups G for which a positive proportion of G-extensions of k fail the Hasse norm principle. We obtain a similar classification for the failure of weak approximation for the associated norm one tori. These results involve counting abelian extensions of bounded discriminant with infinitely many local conditions imposed, which we achieve using tools from harmonic analysis, building on work of Wright.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:60488
Publisher:John Hopkins University Press

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