The Mathematical Institute, University of Oxford, Eprints Archive

The density of rational points on non-singular hypersurfaces, II

Heath-Brown, D. R. and Browning, T. D. (2006) The density of rational points on non-singular hypersurfaces, II. Proceddings of the London Mathematical Society, (3), 93 . pp. 273-303.

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Abstract

For any integers $d,n \geq 2$, let $X \subset \mathbb{P}^{n}$ be a non-singular hypersurface of degree $d$ that is defined over $\mathbb{Q}$. The main result in this paper is a proof that the number $N_X(B)$ of $\mathbb{Q}$-rational points on $X$ which have height at most $B$ satisfies

$
N_X(B)=O_{d,\varepsilon,n}(B^{n-1+\varepsilon}),
$

for any $\varepsilon>0$. The implied constant in this estimate depends at most upon $d, \varepsilon$ and $n$.

Item Type:Article
Additional Information:This is a pre-print version. The original journal should be consulted for the final version
Subjects:H - N > Number theory
Research Groups:Number Theory Group
ID Code:276
Deposited By:Roger Heath-Brown
Deposited On:07 Sep 2006
Last Modified:20 Jul 2009 14:19

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