Polynomial bounds for the solutions of a class of diophantine equations

DOI10.1006/jnth.1997.2153zbMath0894.11011OpenAlexW2029310755MaRDI QIDQ1372593

Dimitrios Poulakis

Publication date: 18 November 1997

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

Full work available at URL: https://doi.org/10.1006/jnth.1997.2153

zbMATH Keywords

algebraic curvespolynomial diophantine equationsPuiseux expansionspolynomial bounds for the height of integer points

Mathematics Subject Classification ID

Diophantine inequalities (11D75)

Related Items (5)

Thue equations and CM-fields ⋮ On the global distance between two algebraic points on a curve. ⋮ Bounds for the smallest integral point on a conic over a number field ⋮ Explicit Chevalley-Weil theorem for affine plane curves ⋮ An Algorithmic Implementation of Runge’s Method for Cubic Diophantine Equations

Cites Work

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• An inequality on the greatest roots of a polynomial
• Integer points and models of algebraic curves
• Effective estimation of integer points of a family of algebraic curves
• Effective analysis of integral points on algebraic curves
• An upper bound for the size of integral solutions to \(Y^ m= f(X)\)
• On the distance between the roots of a polynomial
• Determination of Bounds for the Solutions to those Binary Diophantine Equations that Satisfy the Hypotheses of Runge's Theorem
• On Puiseux series whose curves pass through an infinity of algebraic lattice points
• Eisenstein's theorem on power series expansions of algebraic functions
• A quantitative version of Runge's theorem on diophantine equations
• Bounds for the solutions of Thue-Mahler equations and norm form equations

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