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1 results

Weak approximation on the norm one torus
Part of
P. Koymans, N. Rome
Journal:

Compositio Mathematica / Volume 160 / Issue 6 / June 2024

Published online by Cambridge University Press:

06 May 2024, pp. 1304-1348

Print publication:

June 2024
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For any abelian group $A$, we prove an asymptotic formula for the number of $A$-extensions $K/\mathbb {Q}$ of bounded discriminant such that the associated norm one torus $R_{K/\mathbb {Q}}^1 \mathbb {G}_m$ satisfies weak approximation. We are also able to produce new results on the Hasse norm principle and to provide new explicit values for the leading constant in some instances of Malle's conjecture.