Optimal systems of fundamental \(S\)-units for LLL-reduction

DOI10.1007/s10998-009-9053-xzbMath1199.11135arXiv0905.0745OpenAlexW2008886287MaRDI QIDQ987569

Lajos Hajdu

Publication date: 13 August 2010

Published in: Periodica Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.0745

zbMATH Keywords

\(S\)-unit equationsfundamental system of \(S\)-unitsLLL-reduction

Mathematics Subject Classification ID

Units and factorization (11R27) Computer solution of Diophantine equations (11Y50) Exponential Diophantine equations (11D61)

Related Items (3)

Characterizations of strongly regular rings, II ⋮ Solving 𝑆-unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture ⋮ Parallel LLL-reduction for bounding the integral solutions of elliptic Diophantine equations

Uses Software

• KANT/KASH
• Magma
• PARI/GP

Cites Work

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• Improved Methods for Calculating Vectors of Short Length in a Lattice, Including a Complexity Analysis
• Bounds for the solutions of S-unit equations and decomposable form equations
• Determining the small solutions to 𝑆-unit equations
• Index form equations in quintic fields
• On the Elliptic Logarithm Method for Elliptic Diophantine Equations: Reflections and an Improvement
• Index form equations in sextic fields: a hard computation
• The Solution of Triangularly Connected Decomposable Form Equations
• P-adic logarithmic forms and group varieties III

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