Large Pólya groups in simplest cubic fields and consecutive bi-qaudratic fields

2023/12/05 by Md. Imdadul Islam, Islam, Md. Imdadul, Jaitra Chattopadhyay +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2312.02777

openalex publication_date 2023/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Pólya group of an algebraic number field is the subgroup generated by the ideal classes of the products of prime ideals of equal norm inside the ideal class group. Inspired by a recent work on consecutive quadratic fields with large class numbers by Cherubini et al., we extend the notion of \it consecutiveness of number fields to certain parametric families of cyclic cubic fields and bi-quadratic fields and address the question of the existence of infinitely many such consecutive fields with large Pólya groups. This extends a recent result of the second author and Saikia for totally real bi-quadratic fields.

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• Some bi-quadratic Pólya fields and large Pólya groups of compositum of simplest cubic and quintic fields

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