Arithmetic of octahedral sextics

DOI10.1016/J.JNT.2014.05.023zbMATH Open1300.11108OpenAlexW2007893695MaRDI QIDQ741682

Siman Wong

Publication date: 12 September 2014

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2014.05.023

zbMATH Keywords

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Mathematics Subject Classification ID

Galois theory (11R32) Other number fields (11R21) Cubic and quartic extensions (11R16) Class numbers, class groups, discriminants (11R29) Polynomials (irreducibility, etc.) (11R09)

Cites Work

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• Error estimates for the Davenport-Heilbronn theorems
• \(S_4\) and \(\widetilde{S}_4\) extensions of \(\mathbb{Q}\) ramified at only one prime
• On unramified Galois extensions of quadratic number fields
• The transitive groups of degree up to eleven⁺
• On Totally Real Cubic Fields with Discriminant D < 10 7
• Errata: “On the computation of a table of complex cubic fields with discriminant 𝐷>-10⁶” [Math. Comp. 55 (1990), no. 191, 313–325; MR1023760 (90m:11155)]
• On the Density of Discriminants of Cubic Fields
• On the density of discriminants of cubic fields. II
• Algorithmic Number Theory

Related Items (4)

Octahedral extensions with a given cubic subfield ⋮ Dirichlet series associated to quartic fields with given cubic resolvent ⋮ Proof of a conjecture of Wong concerning octahedral Galois representations of prime power conductor ⋮ Solving the octic by iteration in six dimensions

Uses Software

• nftables
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