Counting rational points on the Cayley ruled cubic
نویسندگان
چکیده
منابع مشابه
Counting Rational Points on Ruled Varieties
In this paper, we prove a general result computing the number of rational points of bounded height on a projective variety V which is covered by lines. The main technical result used to achieve this is an upper bound on the number of rational points of bounded height on a line. This upper bound is such that it can be easily controlled as the line varies, and hence is used to sum the counting fu...
متن کاملCounting 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.
متن کاملCounting Rational Points on Cubic Hypersurfaces: Corrigendum
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....
متن کاملThe Density of Rational Points on Cayley ’ s Cubic Surface
The Cayley cubic surface is given by the equation 4 i=1 X −1 i = 0. We show that the number of non-trivial primitive integer points of size at most B is of exact order B(log B) 6 , as predicted by Manin's conjecture.
متن کاملCounting rational points on ruled varieties over function fields
Let K be the function field of an algebraic curve C defined over a finite field Fq. Let V ⊂ PK be a projective variety which is a union of lines. We prove a general result computing the number of rational points of bounded height on V/K. We first compute the number of rational points on a general line defined over K, and then sum over the lines covering V . Mathematics Subject Classification: 1...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Mathematics
سال: 2015
ISSN: 2199-675X,2199-6768
DOI: 10.1007/s40879-015-0049-1