Counting rational points on smooth cubic curves
نویسندگان
چکیده
منابع مشابه
Counting Rational Points on Cubic Hypersurfaces
Let X ⊂ P be a geometrically integral cubic hypersurface defined over Q, with singular locus of dimension 6 dimX − 4. Then the main result in this paper is a proof of the fact that X(Q) contains Oε,X(B ) points of height at most B.
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R0<b162R0 gcd(b1, N )1/2 R 0 (HP) . The second line is false and in fact one has M1 = 1 in Proposition 3. The author is very grateful to Professor Hongze Li for drawing his attention to this flaw. The error can be fixed by introducing an average over b1 into the statement of Proposition 3. This allows us to recover the main theorem in [1], and also [2, Lemma 11], via the following modification....
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A conjecture of Serre concerns the number of rational points of bounded height on a finite cover of projective space Pn−1. In this paper, we achieve Serre’s conjecture in the special case of smooth cyclic covers of any degree when n ≥ 10, and surpass it for covers of degree r ≥ 3 when n > 10. This is achieved by a new bound for the number of perfect r-th power values of a polynomial with nonsin...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2018
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2017.12.001