Pólya group in some real biquadratic fields

Maarefparvar, Abbas

doi:10.1016/j.jnt.2021.04.012

Cited by 8 publications

(3 citation statements)

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“…If there exist infinitely many pairs of consecutive integers with the same number of prime factors appearing in odd exponents, then by using Proposition 2.1 we would be able to conclude that the answer to Question 6.2 is also 0. For example, the pairs of integers (21,22), (33,34), (34,35), (38,39) and possibly more are admissible choice for such consecutive pairs. In view of this, we ask the following question, an affirmative answer to which will resolve Question 6.2.…”

Section: Discussionmentioning

confidence: 99%

A brief survey of recent results on Pólya groups

Chattopadhyay¹,

Saikia²

2023

Preprint

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The Pólya group of an algebraic number field is a particular subgroup of the ideal class group. This article provides an overview of recent results on Pólya groups of number fields, their connection with the ring of integer-valued polynomials and touches upon some results on number fields having large Pólya groups. For the sake of completeness, we have included the proof of Zantema's theorem which laid the foundation to determine the Pólya groups of many finite Galois extensions over Q. Towards the end of the article, we provide an elementary proof of a weaker version of a recent result of Cherubini et al.

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Section: Discussionmentioning

confidence: 99%

A brief survey of recent results on Pólya groups

Chattopadhyay¹,

Saikia²

2023

Preprint

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“…We aim to relativize the above result of Hilbert for general number fields and for that we need to introduce the notion of relative Pólya groups (recently defined independently in [6] and [15], as a generalization of Pólya groups): Definition 1.6. Let L/E be a finite extension of number fields.…”

Section: Introductionmentioning

confidence: 99%

On quadratic Ostrowski extensions of imaginary quadratic fields

Naroui

Rajaei

2023

Ramanujan J

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“…The main goal of this paper is to generalize this result to the relative setting. The Pólya group has been relativized as follows [3,6]: Definition 1.3. Let L/K be a finite extension of number fields.…”

Section: Introductionmentioning

confidence: 99%