On calculating the number \(N(D)\) of global cubic fields \(F\) of given discriminant \(D\)

DOI10.1016/j.jnt.2021.08.017zbMath1493.11159OpenAlexW3208508757WikidataQ114156744 ScholiaQ114156744MaRDI QIDQ2116770

István Gaál, Michael E. Pohst

Publication date: 18 March 2022

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2021.08.017

zbMATH Keywords

conductordiscriminantJacobi symbolray class group

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Algebraic number theory computations (11Y40) Cubic and quartic extensions (11R16)

Uses Software

• Magma

Cites Work

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• Discovering mathematics with Magma. Reducing the abstract to the concrete
• On computing integral points of a Mordell curve over rational function fields in characteristic \(>3\)
• On computing non-Galois cubic global function fields of prescribed discriminant in characteristic $>3$
• Construction of all cubic function fields of a given square-free discriminant
• On quadratic fields with large 3-rank
• On computing integral points of a Mordell curve – the method of Wildanger revisited

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