Some non-Pólya biquadratic fields with low ramification
type: Item
instance of: scholarly article
title: Some non-Pólya biquadratic fields with low ramification
zbMATH Open document ID: 1433.11121
DOI: 10.4171/RMI/963
author: Bahar Heidaryan
author: Ali Rajaei
published in: Revista Matemática Iberoamericana
publication date: 2017-11-03T00:00:00Z
review text: Summary: Pólya fields are fields with principal Bhargava factorial ideals, and as a generalization of class number one number fields, their classification might be of interest to number theorists. It is known that Pólya fields have little ramification, and the aim of this paper is to prove non-Pólyaness of an infinite family of biquadratic number fields with 3 or 4 primes of ramification, correcting a minor mistake in the literature. It turns out that finer arithmetic invariants of the field such as the Hasse unit index plays a direct role in some cases.
Mathematics Subject Classification ID: 11R04
Mathematics Subject Classification ID: 11R20
Mathematics Subject Classification ID: 11R29
zbMATH DE Number: 6802912
zbMATH Keywords: Pólya fields
zbMATH Keywords: biquadratic fields
zbMATH Keywords: integer-valued polynomials
zbMATH Keywords: Hasse unit index
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/rmi/963
OpenAlex ID: W2761119787
description: scientific article; zbMATH DE number 6802912