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2024 | OriginalPaper | Chapter

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

Authors : Srilakshmi Krishnamoorthy, Sunil Kumar Pasupulati, R. Muneeswaran

Published in: Class Groups of Number Fields and Related Topics

Publisher: Springer Nature Singapore

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Abstract

The chapter delves into the intricate properties of class numbers in quadratic fields, a fundamental topic in algebraic number theory. It begins with an introduction to the ideal class group and the class number, highlighting Gauss's conjectures on the divisibility of class numbers. The text then explores the Cohen-Lenstra heuristics and various conjectures by Chowla, Friedlander, and others. Notably, it covers quantitative results on the divisibility of class numbers, including theorems by Soundararajan and Murty, and advancements in understanding the indivisibility of class numbers. The chapter also discusses recent developments towards Iizuka's conjecture and the 3-divisibility of class numbers, providing a thorough overview of the state-of-the-art in the field. Additionally, it offers insights into the connection between class numbers and special values of L-functions, making it a valuable resource for researchers and scholars interested in the latest advancements in algebraic number theory.

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previous chapter Triples, Quadruples and Quintuples Which are D(n)-Sets for Several n’s

next chapter Congruent Numbers and Class Groups of Associated Quadratic Fields

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Title: A Collage of Results on the Divisibility and Indivisibility of Class Numbers of Quadratic Fields
Authors: Srilakshmi Krishnamoorthy
Sunil Kumar Pasupulati
R. Muneeswaran
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_6

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