Integer points and the rank of Thue elliptic curves

DOI10.1007/BF01389220zbMath0494.14008OpenAlexW2164606848MaRDI QIDQ1169011

Joseph H. Silverman

Publication date: 1982

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142889

zbMATH Keywords

elliptic curvesMordell-Weil groupcubic formThue-Siegel-Roth theoremrank of group of rational points

Mathematics Subject Classification ID

Rational points (14G05) Elliptic curves over global fields (11G05) Arithmetic ground fields for abelian varieties (14K15) Cubic and quartic Diophantine equations (11D25) Approximation to algebraic numbers (11J68)

Related Items (14)

On large values of binary forms ⋮ The canonical height and integral points on elliptic curves ⋮ Representations of integers by binary forms and the rank of the Mordell- Weil group ⋮ On the Parshin-Arakelov theorem and integral sections on elliptic surfaces ⋮ Finiteness criteria and uniformity of integral sections in some families of abelian varieties ⋮ Integral points and the rank of elliptic curves over imaginary quadratic fields ⋮ ON THE NUMBER OF INTEGER POINTS ON THE ELLIPTIC CURVE y² = x³ + Ax ⋮ Elliptic Curves of Bounded Degree and Height ⋮ Primitive Divisors on Twists of Fermat's Cubic ⋮ Generators and integral points on twists of the Fermat cubic ⋮ Unnamed Item ⋮ On equations in S-units and the Thue-Mahler equation ⋮ Lower bounds for height functions ⋮ Enumerating solutions to 𝑝(𝑎)+𝑞(𝑏)=𝑟(𝑐)+𝑠(𝑑)

Cites Work

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• AN EFFECTIVE REFINEMENT OF THE EXPONENT IN LIOUVILLE'S THEOREM
• A sharpening of the bounds for linear forms in logarithms II
• HEIGHT ON FAMILIES OF ABELIAN VARIETIES
• On the Lattice Points on Curves of Genus 1
• Rational approximations to algebraic numbers
• On the representation of integers by binary forms

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