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

### 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 $n$

Topics: Number theory
Year: 2006
OAI identifier: oai:generic.eprints.org:276/core69

### Citations

1. (1977). and S.Kleiman, Foundations of the theory of Fano schemes.
2. (1998). Intersection theory. 2nd ed.,
3. (1943). The maximal number of lines lying on a quartic surface.

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