On Pólya groups of some non-Galois number fields

Abbas Maarefparvar

paper

On Pólya groups of some non-Galois number fields

arXiv:2408.09019

Abstract

We prove two conjectures proposed by Chabert and Halberstadt concerning Pólya groups of $S_{4}$ -fields and $D_{4}$ -fields. More generally, the latter will be proved for $D_{n}$ -fields with $n \geq 4$ an even integer. Further, generalizing a result of Zantema, we also prove that the pre-Pólya group of a non-Galois field of a prime degree, e.g. an $A_{5}$ -field, coincides with its Pólya group.