Computing all monogeneous mixed dihedral quartic extensions of a quadratic field

DOI10.5802/jtnb.310zbMath1065.11086OpenAlexW2318402055MaRDI QIDQ1826289

Gábor Nyul, István Gaál

Publication date: 5 August 2004

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_2001__13_1_137_0

zbMATH Keywords

power integral basisquadratic subfielddihedral quartic field

Mathematics Subject Classification ID

Quadratic extensions (11R11) Thue-Mahler equations (11D59) Computer solution of Diophantine equations (11Y50) Algebraic number theory computations (11Y40) Other abelian and metabelian extensions (11R20)

Uses Software

• KANT/KASH

Cites Work

• On the resolution of index form equations in biquadratic number fields. I
• On the resolution of index form equations in biquadratic number fields. II
• Solving Thue equations of high degree
• Power bases in dihedral quartic fields
• On the resolution of index form equations in quartic number fields
• KANT V4
• On the resolution of index form equations in biquadratic number fields. III: The bicyclic biquadratic case
• Simultaneous representation of integers by a pair of ternary quadratic forms -- with an application to index form equations in quartic number fields
• An Elementary Test for the Galois Group of a Quartic Polynomial
• On the Resolution of Index Form Equations in Dihedral Quartic Number Fields

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