Heuristics for 2-class Towers of Cyclic Cubic Fields

DOI10.1080/10586458.2021.2011492arXiv2012.14824OpenAlexW4205495592MaRDI QIDQ6192601

Michael R. Bush, Nigel Boston

Publication date: 11 March 2024

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.14824

zbMATH Keywords

class field towerideal class groupCohen-Lenstra heuristicscyclic cubic field

Mathematics Subject Classification ID

Cubic and quartic extensions (11R16) Class numbers, class groups, discriminants (11R29)

Cites Work

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• Cohen-Lenstra heuristic and roots of unity
• The distribution of \(p\)-torsion in degree \(p\) cyclic fields
• Isomorphism testing for \(p\)-groups
• The Magma algebra system. I: The user language
• The \(p\)-group generation algorithm
• Random matrices, the Cohen-Lenstra heuristics, and roots of unity
• A class group heuristic based on the distribution of 1-eigenspaces in matrix groups
• Heuristics for \(p\)-class towers of imaginary quadratic fields
• Galois groups of tamely ramified \(p\)-extensions
• Invariants for A₄ fields and the Cohen–Lenstra heuristics
• On the Distribution of Class Groups of Number Fields
• Classnumbers and unit signatures

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