## Abstract

Let K/k be an extension of number fields. We describe theoretical results and computational methods for calculating the obstruction to the Hasse norm principle for K/k and the defect of weak approximation for the norm one torus <![CDATA[ \[R_{K/k}^1{\mathbb{G}_m}\] ]]>. We apply our techniques to give explicit and computable formulae for the obstruction to the Hasse norm principle and the defect of weak approximation when the normal closure of K/k has symmetric or alternating Galois group.

Original language | English |
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Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

DOIs | |

Publication status | Accepted/In press - 2021 |

## Keywords

- 11E72
- 11R37
- 14G05
- 2020 Mathematics Subject Classification:
- 20G30

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