Rational points on diagonal quartic surfaces
نویسندگان
چکیده
منابع مشابه
Rational points on diagonal quartic surfaces
We searched up to height 107 for rational points on diagonal quartic surfaces. The computations fill several gaps in earlier lists computed by Pinch, Swinnerton-Dyer, and Bright.
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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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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2012
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2011-02500-7