Abelian number fields with frobenian conditions

TL;DR

This paper investigates the distribution of abelian number fields under frobenian conditions, providing asymptotic counts for fields with conductors satisfying specific algebraic properties and exploring applications to quadratic fields.

Contribution

It introduces new asymptotic formulas for counting abelian extensions with conductors meeting frobenian conditions, including sums of squares, and applies stack theory to quadratic fields.

Findings

Asymptotic count for abelian fields with conductors as sums of squares

Application of Brauer group of stacks to quadratic fields

Distribution results under frobenian conditions

Abstract

We study the distribution of abelian number fields with frobenian conditions imposed on the conductor. In particular we find an asymptotic for the number of abelian field extensions of a number field k whose conductor is the sum of two squares. We also discuss an application of the Brauer group of stacks to quadratic number fields.