On computing integral points of a Mordell curve over rational function fields in characteristic \(>3\)

DOI10.1016/j.jnt.2012.08.012zbMath1309.11088OpenAlexW2091135058MaRDI QIDQ1930127

Claus Fieker, István Gaál, Michael E. Pohst

Publication date: 10 January 2013

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2012.08.012

zbMATH Keywords

global function fieldsMordell's equation

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Computer solution of Diophantine equations (11Y50) Cubic and quartic Diophantine equations (11D25) Exponential Diophantine equations (11D61)

Related Items (5)

Mordell’s equation: a classical approach ⋮ Construction of all cubic function fields of a given square-free discriminant ⋮ Solving 𝑆-unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture ⋮ Cubic function fields with prescribed ramification ⋮ On calculating the number \(N(D)\) of global cubic fields \(F\) of given discriminant \(D\)

Uses Software

• KANT/KASH
• Magma

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Explicit construction of integral bases of radical function fields
• Discovering mathematics with Magma. Reducing the abstract to the concrete
• Diophantine equations over global function fields. I: The Thue equation
• KANT V4
• Diophantine equations over global function fields. IV: S-unit equations in several variables with an application to norm form equations
• On computing non-Galois cubic global function fields of prescribed discriminant in characteristic $>3$
• Diophantine Equations over Global Function Fields II:R-Integral Solutions of Thue Equations
• ON DAVENPORT-STOTHERS INEQUALITIES AND ELLIPTIC SURFACES IN POSITIVE CHARACTERISTIC

This page was built for publication: On computing integral points of a Mordell curve over rational function fields in characteristic \(>3\)