Journal article icon

Journal article

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 $n$.

Actions


Access Document


Files:

Authors


D. R. Heath-Brown More by this author
T. D. Browning More by this author
Publication date:
2006
URN:
uuid:be99fdc6-8d88-4134-ad3d-31a44a848419
Local pid:
oai:eprints.maths.ox.ac.uk:276

Terms of use


Metrics



If you are the owner of this record, you can report an update to it here: Report update to this record

TO TOP