Genus one curves defined by separated variable polynomials and a polynomial Pell equation

DOI10.4064/aa99-3-2zbMath1025.11005OpenAlexW1977816843MaRDI QIDQ2759130

Umberto Zannier, Roberto M. Avanzi

Publication date: 11 December 2001

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/aa99-3-2

zbMATH Keywords

elliptic curves

Mathematics Subject Classification ID

Polynomials in number theory (11C08) Special algebraic curves and curves of low genus (14H45)

Related Items (21)

On rational functions sharing the measure of maximal entropy ⋮ The relative Riemann–Hurwitz formula ⋮ Algebraic curvesP(x) −Q(y) = 0 and functional equations ⋮ HEIGHTS OF FUNCTION FIELD POINTS ON CURVES GIVEN BY EQUATIONS WITH SEPARATED VARIABLES ⋮ Canonical heights for correspondences ⋮ Unlikely Intersections and Pell’s Equations in Polynomials ⋮ Uniqueness theorems for differential polynomials sharing a small function ⋮ The Diophantine equation f(x)=g(y)$f(x)=g(y)$ for polynomials with simple rational roots ⋮ Variables separated equations: strikingly different roles for the branch cycle lemma and the finite simple group classification ⋮ On algebraic curves \(A(x)-B(y)=0\) of genus zero ⋮ Unnamed Item ⋮ Genus one factors of curves defined by separated variable polynomials ⋮ Unnamed Item ⋮ Normality and uniqueness property of meromorphic function in terms of some differential polynomials ⋮ Finite Weil restriction of curves ⋮ On special extrema of polynomials with applications to Diophantine problems ⋮ Pseudo-elliptic integrals, units, and torsion ⋮ Powers in Orbits of Rational Functions: Cases of an Arithmetic Dynamical Mordell–Lang Conjecture ⋮ Ritt's theory on the unit disk ⋮ The polynomial Pell equation ⋮ Specialisation and reduction of continued fractions of formal power series

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