Rational points on diagonal quartic surfaces

DOI10.1090/S0025-5718-2011-02500-7zbMath1234.14019arXiv1008.3275MaRDI QIDQ3117220

Andreas-Stephan Elsenhans

Publication date: 17 February 2012

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.3275

zbMATH Keywords

rational point\(K3\) surfacehashingDiophantine equationquartic equationcomputer solutiondiagonal quartic surface

Mathematics Subject Classification ID

Rational points (14G05) Computer solution of Diophantine equations (11Y50) (K3) surfaces and Enriques surfaces (14J28) Varieties over global fields (11G35) Cubic and quartic Diophantine equations (11D25) Special surfaces (14J25)

Related Items (1)

Constructions of diagonal quartic and sextic surfaces with infinitely many rational points

Cites Work

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• Rational points of bounded height on Fano varieties
• Heights and Tamagawa measures on Fano varieties
• On the Brauer group of diagonal quartic surfaces
• The Brauer–Manin obstruction on a general diagonal quartic surface
• Forms in many variables
• The Diophantine Equation 𝑥⁴+2𝑦⁴=𝑧⁴+4𝑤⁴
• Enumerating solutions to 𝑝(𝑎)+𝑞(𝑏)=𝑟(𝑐)+𝑠(𝑑)
• Rational Points on Some Fano Quadratic Bundles
• Algorithmic Number Theory

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