Corpus ID: 119622254

Number fields with prescribed norms.

  title={Number fields with prescribed norms.},
  author={Christopher Frei and Daniel Loughran and Rachel Newton and with an appendix by Yonatan Harpaz and Olivier Wittenberg},
  journal={arXiv: Number Theory},
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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