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2024 | OriginalPaper | Chapter

Fundamental Systems of Units of Some Imaginary Multiquadratic Fields of Degree 16

Authors : Abdelmalek Azizi, Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini

Published in: Applied Mathematics and Modelling in Finance, Marketing and Economics

Publisher: Springer Nature Switzerland

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Abstract

Let \(q_1\equiv q_2\equiv 3\pmod 8\) be two different prime integers, d a positive odd square-free integer relatively prime to \(q_1\) and \(q_2\). The main aim of this paper is to investigate the unit groups of some number fields of the form \(\mathbb {L}=\mathbb {Q}(\sqrt{2}, \sqrt{q_1}, \sqrt{q_2}, \sqrt{-d})\).

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Literature
1.
Azizi, A.: Unités de certains corps de nombres imaginaires et abéliens sur \(\mathbb{Q} \). Ann. Sci. Math. Québec. 23, 15–21 (1999)MathSciNet
2.
Chems-Eddin, M.M.: Unit groups of some multiquadratic number fields and \(2\)-class groups. Period. Math. Hung. 84, 235–249 (2022)
3.
Chems-Eddin, M.M., Azizi, A., Zekhnini, A.: Unit groups and Iwasawa lambda invariants of some multiquadratic number fields. Bol. Soc. Mat. Mex. III. Ser. 27 (2021), Article ID 24, 16 pages
4.
Chems-Eddin, M.M., Zekhnini, A., Azizi, A.: Units and \(2\)-class field towers of some multiquadratic number fields. Turk. J. Math. 44, 1466–1483 (2020)MathSciNetCrossRef
5.
Chems-Eddin, M.M., Zekhnini, A., Azizi, A.: On the Hilbert \(2\)-class field towers of some cyclotomic \(\mathbb{Z}_2\)-extensions. arXiv:​2005.​06646
6.
Kubota, T.: Über den bizyklischen biquadratischen Zahlkörper. Nagoya Math. J. 10, 65–85 (1956) (in German)
7.
Wada, H.: On the class number and the unit group of certain algebraic number fields. J. Fac. Univ. Tokyo. 13, 201–209 (1966)
Metadata
Title
Fundamental Systems of Units of Some Imaginary Multiquadratic Fields of Degree 16
Authors
Abdelmalek Azizi
Mohamed Mahmoud Chems-Eddin
Abdelkader Zekhnini
Copyright Year
2024
Book
Applied Mathematics and Modelling in Finance, Marketing and Economics

Print ISBN: 978-3-031-42846-3

Electronic ISBN: 978-3-031-42847-0

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-42847-0_11

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