When Newton met Diophantus: a study of rational-derived polynomials and their extension to quadratic fields.

DOI10.1006/jnth.1999.2473zbMath1035.11009OpenAlexW1974337041MaRDI QIDQ1976804

Ralph H. Buchholz, J. A. MacDougall

Publication date: 11 January 2001

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

Full work available at URL: https://semanticscholar.org/paper/a7d80838ed50ffa6a9c3d5fd44803f070e7e804c

zbMATH Keywords

hyperelliptic curvederivativeelliptic curvepolynomialquartic Diophantine equationJacobian varietyalgebraic surface

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Polynomials in number theory (11C08) Elliptic curves (14H52) Jacobians, Prym varieties (14H40) Elliptic surfaces, elliptic or Calabi-Yau fibrations (14J27) [https://portal.mardi4nfdi.de/w/index.php?title=+Special%3ASearch&search=%22Curves+of+arbitrary+genus+or+genus+%28%0D%0Ae+1%29+over+global+fields%22&go=Go Curves of arbitrary genus or genus ( e 1) over global fields (11G30)] Cubic and quartic Diophantine equations (11D25) Polynomials (irreducibility, etc.) (11R09) Higher degree equations; Fermat's equation (11D41) Special surfaces (14J25)

Related Items (4)

On \(K\)-derived quartics ⋮ On \(\mathbb Q\)-derived polynomials ⋮ Building the Biggest Box: Three-factor Polynomials and a Diophantine Equation ⋮ A diophantine problem from calculus

Cites Work

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• Cubic Equations, or Where Did the Examination Question Come From?
• Descent via isogeny in dimension 2
• A Diophantine Equation from Calculus
• On rational-derived quartics

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