Calculating all elements of minimal index in the infinite parametric family of simplest quartic fields

DOI10.1007/s10587-014-0113-xzbMath1340.11102arXiv1810.00060OpenAlexW3099356444MaRDI QIDQ2940656

István Gaál, Gábor Petrányi

Publication date: 27 January 2015

Published in: Czechoslovak Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.00060

zbMATH Keywords

monogeneitypower integral basesimplest quartic field

Mathematics Subject Classification ID

Computer solution of Diophantine equations (11Y50) Cubic and quartic extensions (11R16) Algebraic numbers; rings of algebraic integers (11R04) Multiplicative and norm form equations (11D57)

Related Items (3)

Integral bases and monogenity of the simplest sextic fields ⋮ Monogenity in totally real extensions of imaginary quadratic fields with an application to simplest quartic fields ⋮ Index, the prime ideal factorization in simplest quartic fields and counting their discriminants

Uses Software

• KANT/KASH
• Maple

Cites Work

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• Establishing the minimal index in a parametric family of bicyclic biquadratic fields
• KANT V4
• A parametric family of quintic Thue equations. II
• Simultaneous representation of integers by a pair of ternary quadratic forms -- with an application to index form equations in quartic number fields
• Complete solution of a family of quartic Thue equations
• The Simplest Cubic Fields
• Simple families of Thue inequalities
• Power integral bases in a parametric family of totally real cyclic quintics
• Power Integral Bases in the Family of Simplest Quartic Fields
• On the class number and unit index of simplest quartic fields

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