Solving index form equations in fields of degree 9 with cubic subfields

DOI10.1006/jsco.1999.0356zbMath0983.11077OpenAlexW2029447385MaRDI QIDQ1582301

István Gaál

Publication date: 23 April 2002

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jsco.1999.0356

zbMATH Keywords

effective algorithmindex form equationscubic relative Thue equations

Mathematics Subject Classification ID

Thue-Mahler equations (11D59) Computer solution of Diophantine equations (11Y50) Multiplicative and norm form equations (11D57)

Related Items (7)

Power Integral Bases in Orders of Composite Fields ⋮ On biquadratic fields that admit unit power integral basis ⋮ On unit power integral bases of \(\mathbb Z[\root 4 \of {m}\)] ⋮ Power Integral Bases in Cubic Relative Extensions ⋮ Calculating power integral bases by using relative power integral bases ⋮ Application of Weierstrass units to relative power integral bases ⋮ Calculating “Small” Solutions of Relative Thue Equations

Cites Work

• On the resolution of index form equations in sextic fields with an imaginary quadratic subfield
• On the resolution of index form equations in quartic number fields
• Computing elements of given index in totally complex cyclic sextic fields
• Simultaneous representation of integers by a pair of ternary quadratic forms -- with an application to index form equations in quartic number fields
• Solving discriminant form equations via unit equations
• Logarithmic forms and group varieties.
• On the Resolution of Inhomogeneous Norm Form Equations in Two Dominating Variables
• Power Integral Bases in Composits of Number Fields
• Bounds for the solutions of unit equations
• Computing all power integral bases in orders of totally real cyclic sextic number fields
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²
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