On integral points on surfaces
نویسندگان
چکیده
منابع مشابه
Integral Points on Punctured Abelian Surfaces
We study the density of integral points on punctured abelian surfaces. Linear growth rates are observed experimentally.
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Let g ∈ Z[x1, . . . , xn] be an absolutely irreducible cubic polynomial whose homogeneous part is non-degenerate. The primary goal of this paper is to investigate the set of integer solutions to the equation g = 0. Specifically, we shall try to determine conditions on g under which we can show that there are infinitely many solutions. An obvious necessary condition for the existence of integer ...
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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: Annals of Mathematics
سال: 2004
ISSN: 0003-486X
DOI: 10.4007/annals.2004.160.705