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Consider the real cyclic quartic number fields \(\mathbb {K}=\mathbb {Q}(\sqrt{n\varepsilon _{0}\sqrt{\ell }})\) , where \(\ell =2\) or \(\ell \equiv 1\pmod 4\) is a prime, n is a square-free positive integer relatively prime to \(\ell \) and \(\varepsilon _{0}\) the fundamental unit of its unique quadratic subfield \(k=\mathbb {Q}(\sqrt{\ell })\) . In this article, we explicitly determine the fundamental system of units of these fields \(\mathbb {K}\) .

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The Fundamental System of Units of Some Real Cyclic Quartic Number Fields

  • 会议论文

  • 发表日期：

    2025年

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  • Abdelmalek Azizi,
  • Mohammed Tamimi,
  • Abdelkader Zekhnini

摘要

Consider the real cyclic quartic number fields \(\mathbb {K}=\mathbb {Q}(\sqrt{n\varepsilon _{0}\sqrt{\ell }})\) , where \(\ell =2\) or \(\ell \equiv 1\pmod 4\) is a prime, n is a square-free positive integer relatively prime to \(\ell \) and \(\varepsilon _{0}\) the fundamental unit of its unique quadratic subfield \(k=\mathbb {Q}(\sqrt{\ell })\) . In this article, we explicitly determine the fundamental system of units of these fields \(\mathbb {K}\) .