# The Hasse norm principle for abelian extensions

@article{Frei2015TheHN,
title={The Hasse norm principle for abelian extensions},
author={C. Frei and Christopher Daniel Rachel Loughran and Christopher Daniel Rachel Newton},
journal={American Journal of Mathematics},
year={2015},
volume={140},
pages={1639 - 1685}
}
• Published 2015
• Mathematics
• American Journal of Mathematics
Abstract: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… Expand
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