Number fields with prescribed norms
arXiv: Number Theory(2022)
Abstract
We study the distribution of extensions of a number field k with fixed abelian Galois group G, from which a given finite set of elements of k are norms. In particular, we show the existence of such extensions. Along the way, we show that the Hasse norm principle holds for 100% of G-extensions of k, when ordered by conductor. The appendix contains an alternative purely geometric proof of our existence result.
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Key words
Hasse norm principle,class field theory,rational points on varieties,harmonic analysis
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