On P\'olya groups of some non-Galois number fields

Abbas Maarefparvar

On P\'olya groups of some non-Galois number fields

Number Theory 2024-08-20 v1

Authors: Abbas Maarefparvar

Abstract

We prove two conjectures proposed by Chabert and Halberstadt concerning P\'olya 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-P\'olya group of a non-Galois field of a prime degree, e.g. an $A_5$ -field, coincides with its P\'olya group.

Keywords

Pólya groups non-Galois number fields S4 fields D4 fields A5 fields

Cite

@article{arxiv.2408.09019,
  title  = {On P\'olya groups of some non-Galois number fields},
  author = {Abbas Maarefparvar},
  journal= {arXiv preprint arXiv:2408.09019},
  year   = {2024}
}

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