On Manin's conjecture for a family of Ch\^atelet surfaces
classification
🧮 math.NT
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surfacesateletconjecturemaninapproximationarisingdegreeestablished
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The Manin conjecture is established for Ch\^atelet surfaces over Q arising as minimal proper smooth models of the surface Y^2+Z^2=f(X) where f is a totally reducible polynomial of degree 3 without repeated roots. These surfaces do not satisfy weak approximation.
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