Explicit methods for the Hasse norm principle and applications to A
n
and S
n
extensions
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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 \[R_{K/k}^1{\mathbb{G}_m}\] . 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.
2016 ◽
Vol 93
(3)
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pp. 420-432
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2009 ◽
Vol 08
(04)
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pp. 493-503
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2015 ◽
Vol 64
(1)
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pp. 21-57
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2012 ◽
Vol 141
(2)
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pp. 499-503
1991 ◽
Vol 43
(5)
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pp. 1086-1097
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2015 ◽
Vol 18
(1)
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pp. 684-698
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2011 ◽
Vol 151
(1)
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pp. 1-22
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