On the resolution of relative Thue equations

DOI10.1090/S0025-5718-01-01329-1zbMath0985.11070OpenAlexW1999631664MaRDI QIDQ2759111

István Gaál, Michael E. Pohst

Publication date: 10 December 2001

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-01-01329-1

zbMATH Keywords

reductionrelative Thue equationenumerationBaker's method

Mathematics Subject Classification ID

Thue-Mahler equations (11D59) Computer solution of Diophantine equations (11Y50)

Related Items (15)

Unnamed Item ⋮ CALCULATING RELATIVE POWER INTEGRAL BASES IN TOTALLY COMPLEX QUARTIC EXTENSIONS OF TOTALLY REAL FIELDS ⋮ Solving genus zero Diophantine equations over number fields ⋮ On a simple quartic family of Thue equations over imaginary quadratic number fields ⋮ ON THE MONOGENITY OF TOTALLY COMPLEX PURE SEXTIC FIELDS ⋮ Simplest quartic and simplest sextic Thue equations over imaginary quadratic fields ⋮ All solutions to Thomas' family of Thue equations over imaginary quadratic number fields ⋮ Power Integral Bases in Cubic Relative Extensions ⋮ On a family of relative quartic Thue inequalities ⋮ Computing power integral bases in quartic relative extensions ⋮ Optimal systems of fundamental \(S\)-units for LLL-reduction ⋮ Calculating ``small solutions of inhomogeneous relative Thue inequalities ⋮ A SYSTEM OF RELATIVE PELLIAN EQUATIONS AND A RELATED FAMILY OF RELATIVE THUE EQUATIONS ⋮ Calculating “Small” Solutions of Relative Thue Equations ⋮ Thomas' family of Thue equations over imaginary quadratic fields

Uses Software

• KANT/KASH

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the resolution of Thue inequalities
• On the resolution of index form equations in sextic fields with an imaginary quadratic subfield
• Solving Thue equations of high degree
• KANT V4
• Computing elements of given index in totally complex cyclic sextic fields
• Logarithmic forms and group varieties.
• Improved Methods for Calculating Vectors of Short Length in a Lattice, Including a Complexity Analysis
• Thue equations with composite fields
• Thue and Thue-Mahler Equations over Rings of Integers
• The Solution of Triangularly Connected Decomposable Form Equations
• A Thue Equation with Quadratic Integers as Variables
• Bounds for the solutions of Thue-Mahler equations and norm form equations
• Computing all power integral bases in orders of totally real cyclic sextic number fields
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²

This page was built for publication: On the resolution of relative Thue equations