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

Mathematics – Number Theory

Scientific paper

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36 pages; appendix by J. Starr

Scientific paper

This paper establishes the conjecture that a non-singular projective
hypersurface of dimension $r$, which is not equal to a linear space, contains
$O(B^{r+\epsilon})$ rational points of height at most $B$, for any choice of
$\epsilon>0$. The implied constant in this estimate depends at most upon
$\epsilon, r$ and the degree of the hypersurface.

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