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2024 | OriginalPaper | Chapter

A Brief Survey of Recent Results on Pólya Groups

Authors : Jaitra Chattopadhyay, Anupam Saikia

Published in: Class Groups of Number Fields and Related Topics

Publisher: Springer Nature Singapore

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Abstract

The Pólya group of a number field is a particular subgroup of the ideal class group of that number field. In this article, we discuss some 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. We include the proof of Zantema’s theorem which laid the foundation to determine the Pólya groups of many finite Galois extensions over \(\mathbb {Q}\). At the end, we provide an elementary proof of a weaker version of a recent result of Cherubini et al.

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previous chapter The Diophantine Equation
next chapter A Note on Sums of Squares in Non-Totally Real Fields
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Metadata
Title
A Brief Survey of Recent Results on Pólya Groups
Authors
Jaitra Chattopadhyay
Anupam Saikia
Copyright Year
2024
Publisher
Springer Nature Singapore
Book
Class Groups of Number Fields and Related Topics

Print ISBN: 978-981-9769-10-0

Electronic ISBN: 978-981-9769-11-7

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-981-97-6911-7_12

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