1 research outputs found
Number fields with prescribed norms
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 of -extensions of
, when ordered by conductor. The appendix contains an alternative purely
geometric proof of our existence result.Comment: 35 pages, comments welcome