Number fields with prescribed norms

Christopher Frei, Daniel Loughran, Rachel Newton

OAI: oai:purehost.bath.ac.uk:openaire_cris_publications/115b7ebc-b7bf-4493-89a0-31b4e29d8273 • DOI: https://doi.org/10.4171/CMH/528

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.

Hasse norm principle class field theory harmonic analysis rational points on varieties /dk/atira/pure/subjectarea/asjc/2600/2600 name=General Mathematics