Tamagawa numbers of diagonal cubic surfaces, numerical evidence

DOI10.1090/S0025-5718-00-01189-3zbMath0961.14012arXivmath/9809054OpenAlexW2167434745MaRDI QIDQ4517529

Yuri Tschinkel, Emmanuel Peyre

Publication date: 22 November 2000

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

Full work available at URL: https://arxiv.org/abs/math/9809054

zbMATH Keywords

algorithmFano varietyasymptotic behaviourPicard groupcounting functiongeometric invariantsBrauer-Manin obstructionTamagawa numbernumber of rational points of bounded heightdiagonal cubic surfacesZbl 0991.72285

Mathematics Subject Classification ID

Rational points (14G05) Heights (11G50) Fano varieties (14J45) Cubic and quartic Diophantine equations (11D25) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

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Cites Work

• Hilbert's theorem 90 for \(K^ 2\), with application to the Chow groups of rational surfaces
• Rational points of bounded height on Fano varieties
• On the number of rational points of bounded height on algebraic varieties
• Une presentation adelique de la série singuliere et du problème de Waring
• Weak approximation for surfaces defined by two quadratic forms
• Heights and Tamagawa measures on Fano varieties
• The Density of Zeros of Forms for which Weak Approximation Fails
• Rational Points of Bounded Height on Compactifications of Anisotropic Tori
• Rational points on some Fano cubic bundles
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