Mathematics – Number Theory
Scientific paper
2005-05-10
Mathematics
Number Theory
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.
Browning T. D.
Heath-Brown D. R.
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