Thomas' family of Thue equations over imaginary quadratic fields

DOI10.1006/jsco.2002.0568zbMath1009.11022OpenAlexW2123442989MaRDI QIDQ1864895

Clemens Heuberger, Robert F. Tichy, Attila Pethoe

Publication date: 23 March 2003

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

Full work available at URL: https://doi.org/10.1006/jsco.2002.0568

zbMATH Keywords

Thue equationsBaker's method

Mathematics Subject Classification ID

Quadratic extensions (11R11) Thue-Mahler equations (11D59) Cubic and quartic Diophantine equations (11D25)

Related Items (10)

Elements of small norm in Shanks' cubic extensions of imaginary quadratic fields ⋮ On a simple quartic family of Thue equations over imaginary quadratic number fields ⋮ Simplest quartic and simplest sextic Thue equations over imaginary quadratic fields ⋮ Parameterized norm form equations with arithmetic progressions ⋮ All solutions to Thomas' family of Thue equations over imaginary quadratic number fields ⋮ On a family of relative quartic Thue inequalities ⋮ On a family of Thue equations over function fields ⋮ A parametric family of cubic Thue equations ⋮ On the family of Thue equation|x 3+mx2y−(m+3)xy2+y3|=k ⋮ A SYSTEM OF RELATIVE PELLIAN EQUATIONS AND A RELATED FAMILY OF RELATIVE THUE EQUATIONS

Uses Software

• PARI/GP

Cites Work

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• The Simplest Cubic Fields
• A corollary to a theorem of Laurent-Mignotte-Nesterenko
• Solutions to infinite families of complex cubic Thue equations.
• Bounds for the solutions of Thue-Mahler equations and norm form equations
• On the solutions of a family of quartic Thue equations
• Contributions to the theory of diophantine equations I. On the representation of integers by binary forms
• On explicit bounds for the solutions of a class of parametrized Thue equations of arbitrary degree

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