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2024 | OriginalPaper | Chapter

Congruent Numbers and Class Groups of Associated Quadratic Fields

Authors : Shamik Das, Anupam Saikia

Published in: Class Groups of Number Fields and Related Topics

Publisher: Springer Nature Singapore

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Abstract

In this article, we first discuss congruent numbers and certain recent results concerning their generalizations. Then we review some recent results concerning the 2-part of the class group of \(\mathbb {Q}(\sqrt{\pm n})\) for a congruent number n. We conclude with a sufficient congruence condition for a prime p so that 2p is non-congruent.

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previous chapter A Collage of Results on the Divisibility and Indivisibility of Class Numbers of Quadratic Fields

next chapter Note on the Rank of 2-Class Group of

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Title: Congruent Numbers and Class Groups of Associated Quadratic Fields
Authors: Shamik Das
Anupam Saikia
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_7

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