Rational Points on Cubic Surfaces
نویسنده
چکیده
Let k be an algebraic number eld and F (x0; x1; x2; x3) a non{singular cubic form with coeecients in k. Suppose that the pro-jective cubic k{surface X P 3 k given by F = 0 contains three coplanar lines deened over k, and let U (k) be the set of k{points on X which does not lie on any line on X. We show that the number of points in U (k), with height at most B, is OF;"(B 4=3+") for any " > 0.
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