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

Abstract

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.

36 pages; appendix by J. Starr