Calculation of the Class Numbers of Imaginary Cyclic Quartic Fields

DOI10.2307/2008334zbMath0624.12004OpenAlexW4229530879MaRDI QIDQ3762412

N. M. Holtz, Kenneth S. Williams, Richard H. Hudson, Kenneth Hardy, David R. Richman

Publication date: 1987

Full work available at URL: https://doi.org/10.2307/2008334

zbMATH Keywords

class numbersimaginary cyclic quartic fieldsdiscriminant formulae

Mathematics Subject Classification ID

Other number fields (11R21) Iwasawa theory (11R23) Software, source code, etc. for problems pertaining to field theory (12-04)

Related Items (18)

To the Hilbert class field from the hypergeometric modular function ⋮ Hopf-Galois module structure of quartic Galois extensions of \(\mathbb{Q}\) ⋮ Icosahedral invariants and a construction of class fields via periods of \(K3\) surfaces ⋮ On the tame kernels of imaginary cyclic quartic fields with class number one ⋮ On tame kernels and second regulators of number fields and their subfields ⋮ EXPLICIT KUMMER THEORY FOR QUADRATIC FIELDS ⋮ Quartic fields with large class numbers ⋮ The2-rankof the class group of some real cyclic quartic number fields II ⋮ On Hilbert genus fields of imaginary cyclic quartic fields ⋮ 5-class towers of cyclic quartic fields arising from quintic reflection ⋮ The shapes of Galois quartic fields ⋮ The integers of a cyclic quartic field ⋮ On the \(p\)-rank of tame kernel of number fields ⋮ Gaussian Periods and Units in Certain Cyclic Fields ⋮ The 2-rank of the class group of some real cyclic quartic number fields ⋮ Number fields with large minimal index containing quadratic subfields ⋮ Kummer theory for multiquadratic or quartic cyclic number fields ⋮ The construction of the Hilbert genus fields of real cyclic quartic fields

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