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

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Applied Mathematics and Modelling in Finance, Marketing and Economics

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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References

  1. Azizi, A.: Unités de certains corps de nombres imaginaires et abéliens sur \(\mathbb{Q} \). Ann. Sci. Math. Québec. 23, 15–21 (1999)

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  2. Chems-Eddin, M.M.: Unit groups of some multiquadratic number fields and \(2\)-class groups. Period. Math. Hung. 84, 235–249 (2022)

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  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

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  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)

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  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)

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  7. Wada, H.: On the class number and the unit group of certain algebraic number fields. J. Fac. Univ. Tokyo. 13, 201–209 (1966)

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Correspondence to Mohamed Mahmoud Chems-Eddin .

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Azizi, A., Chems-Eddin, M.M., Zekhnini, A. (2024). Fundamental Systems of Units of Some Imaginary Multiquadratic Fields of Degree 16. In: Melliani, S., Castillo, O., El Hajaji, A. (eds) Applied Mathematics and Modelling in Finance, Marketing and Economics. Studies in Computational Intelligence, vol 1114. Springer, Cham. https://doi.org/10.1007/978-3-031-42847-0_11

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

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