$\ell$-torsion in class groups of certain families of $D_4$-quartic fields

Chen An

paper

$ℓ$ -torsion in class groups of certain families of $D_{4}$ -quartic fields

arXiv:1808.02148

Abstract

We prove an upper bound for $ℓ$ -torsion in class groups of almost all fields in certain families of $D_{4}$ -quartic fields. Our key tools are a new Chebotarev density theorem for these families of $D_{4}$ -quartic fields and a lower bound for the number of fields in the families.

Version 2: fixed minor errors and updated references. To be published in the Journal de Theorie des Nombres de Bordeaux

ℓ-torsion in class groups of certain families of D4​-quartic fields

Abstract

$ℓ$ -torsion in class groups of certain families of $D_{4}$ -quartic fields