The Fermat cubic and quartic curves over cyclic fields

DOI10.1007/s10998-019-00297-yzbMath1474.14041OpenAlexW2991203948WikidataQ126775243 ScholiaQ126775243MaRDI QIDQ2204116

Ajai Choudhry, Andrew Bremner

Publication date: 2 October 2020

Published in: Periodica Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10998-019-00297-y

zbMATH Keywords

Fermat cubiccyclic cubic number fieldFermat quartic

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Cubic and quartic Diophantine equations (11D25) Global ground fields in algebraic geometry (14G25)

Related Items (5)

Points on x4 + y4 + z4 = 0 over algebraic extensions of ℚ(i) ⋮ The equation \(x^4+2^ny^4=z^4\) in algebraic number fields ⋮ Solutions to \(x^4+py^4=z^4\) in cubic number fields ⋮ On the Diophantine equation $x^4+y^4=c$ ⋮ Fermat quartics with only trivial solutions in any odd degree number field

Cites Work

• Unnamed Item
• Some Quartic Curves with no Points in any Cubic Field
• Algebraic points of low degree on the Fermat quintic
• The arithmetic of certain quartic curves

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