A criterion for a certain type of imaginary quadratic fields to have 3-ranks of the ideal class groups greater than one

DOI10.3792/PJAA.74.93zbMath0930.11080OpenAlexW2056000261MaRDI QIDQ1281657

Yasuhiro Kishi

Publication date: 14 February 2000

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.74.93

zbMATH Keywords

fundamental unitcubic extensionsimaginary quadratic number fieldCardano's formula3-rank of the ideal class group

Mathematics Subject Classification ID

Quadratic extensions (11R11) Class numbers, class groups, discriminants (11R29)

Related Items (5)

Divisibility of class numbers of certain families of quadratic fields ⋮ Imaginary quadratic fields whose ideal class groups have 3-rank at least three ⋮ ON THE IDEAL CLASS GROUP OF CERTAIN QUADRATIC FIELDS ⋮ A constructive approach to Spiegelung relations between 3-ranks of absolute ideal class groups and congruent ones modulo \((3)^2\) in quadratic fields ⋮ Infinite families of class groups of quadratic fields with 3-rank at least one: quantitative bounds

Cites Work

• On fundamental units of real quadratic fields with norm \(+1\)
• Parametrization of the quadratic fields whose class numbers are divisible by three
• Effective Determination of the Decomposition of the Rational Primes in a Cubic Field

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