Abstract

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 conditions imposed, which we achieve using tools from harmonic analysis, building on work of Wright.

pdf

Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1639-1685
Launched on MUSE
2018-11-20
Open Access
No
Back To Top

This website uses cookies to ensure you get the best experience on our website. Without cookies your experience may not be seamless.