On Simultaneous Divisibility of the Class Numbers of Imaginary Quadratic Fields

DOI10.1007/978-981-15-1514-9_2zbMath1444.11220OpenAlexW2999221956MaRDI QIDQ3298281

Toru Komatsu

Publication date: 14 July 2020

Published in: Class Groups of Number Fields and Related Topics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-981-15-1514-9_2

zbMATH Keywords

imaginary quadratic fieldsinverse Galois problemclass numbers

Mathematics Subject Classification ID

Galois theory (11R32) Quadratic extensions (11R11) Inverse Galois theory (12F12) Class numbers, class groups, discriminants (11R29)

Cites Work

• Existence of an infinite family of pairs of quadratic fields \(\mathbb{Q}(\sqrt{m_1D})\) and \(\mathbb{Q}(\sqrt{m_2D})\) whose class numbers are both divisible by 3 or both indivisible by 3
• Explicit construction of a class of infinitely many imaginary quadratic fields whose class number is divisible by 3
• Proof of the existence of infinitely many imaginary quadratic fields whose class number is not divisible by 3
• Real quadratic fields with class numbers divisible by \(n\)
• Sur les nombres de classes de certains corps quadratiques
• On the divisibility of the class number of quadratic fields
• An infinite family of pairs of imaginary quadratic fields with ideal classes of a given order
• An infinite family of pairs of quadratic fields Q(\sqrt D) and Q(\sqrt mD) whose class numbers are both divisible by 3
• On the class number of imaginary quadratic number fields
• On Real Quadratic Fields whose Class Numbers are Multiples of 3.

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