Number fields with prescribed norms (with an appendix by Yonatan Harpaz and Olivier Wittenberg)

  • Christopher Frei

    TU Graz, Austria
  • Daniel Loughran

    University of Bath, UK
  • Rachel Newton

    King’s College London, UK
Number fields with prescribed norms (with an appendix by Yonatan Harpaz and Olivier Wittenberg) cover
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Abstract

We study the distribution of extensions of a number field with fixed abelian Galois group , from which a given finite set of elements of 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 -extensions of , when ordered by conductor. The appendix contains an alternative purely geometric proof of our existence result.

Cite this article

Christopher Frei, Daniel Loughran, Rachel Newton, Number fields with prescribed norms (with an appendix by Yonatan Harpaz and Olivier Wittenberg). Comment. Math. Helv. 97 (2022), no. 1, pp. 133–181

DOI 10.4171/CMH/528