Relative Polya Group and Polya Dihedral Extensions of Q

TL;DR

This paper introduces the concept of the relative Polya group for number field extensions, proves its triviality for Hilbert class fields, and extends previous results on Polya S3-extensions to certain dihedral extensions of Q.

Contribution

It defines the relative Polya group, proves its triviality in specific cases, and generalizes earlier results to dihedral extensions of Q.

Findings

Relative Polya group is trivial for Hilbert class fields.

Extended Polya S3-results to some dihedral extensions.

Provided new insights into Polya properties of number fields.

Abstract

We define the relative Polya group for a finite extension of number fields and prove triviality of the relative Polya group for the Hilbert class field. Then we generalize our previous results on Polya S3-extensions of Q to some dihedral extensions of Q.