THE DENSITY OF RATIONAL POINTS ON NON-SINGULAR HYPERSURFACES, I
نویسندگان
چکیده
منابع مشابه
The density of rational points on non-singular hypersurfaces, I
For any n > 3, let F ∈ Z[X0, . . . , Xn] be a form of degree d > 5 that defines a non-singular hypersurface X ⊂ P. The main result in this paper is a proof of the fact that the number N(F ;B) of Q-rational points on X which have height at most B satisfies N(F ;B) = Od,ε,n(B ), for any ε > 0. The implied constant in this estimate depends at most upon d, ε and n. New estimates are also obtained f...
متن کاملThe density of rational points on non-singular hypersurfaces, II
For any integers d, n ≥ 2, let X ⊂ P be a non-singular hypersurface of degree d that is defined over Q. The main result in this paper is a proof that the number NX(B) of Q-rational points on X which have height at most B satisfies NX(B) = Od,ε,n(B n−1+ε), for any ε > 0. The implied constant in this estimate depends at most upon d, ε and n. Mathematics Subject Classification (2000): 11D45 (11G35...
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For any n 3, let F ∈ Z[X0,. .. , Xn] be a form of degree d 5 that defines a non-singular hypersurface X ⊂ P n. The main result in this paper is a proof of the fact that the number N (F ; B) of Q-rational points on X which have height at most B satisfies N (F ; B) = O d,ε,n (B n−1+ε), for any ε > 0. The implied constant in this estimate depends at most upon d, ε and n. New estimates are also obt...
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For any n ≥ 2, let F ∈ Z[x1, . . . , xn] be a form of degree d ≥ 2, which produces a geometrically irreducible hypersurface in P. This paper is concerned with the number N(F ; B) of rational points on F = 0 which have height at most B. For any ε > 0 we establish the estimate N(F ; B) = O(B), whenever either n ≤ 5 or the hypersurface is not a union of lines. Here the implied constant depends at ...
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2006
ISSN: 0024-6093,1469-2120
DOI: 10.1112/s0024609305018412