2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101261This paper establishes the conjecture that a non-singular projective hypersurface of dimension $r$, which is not equal to a linear space, contains $O(B^{r+ε})$ rational points of height at most $B$, for any choice of $ε>0$. The implied constant in this estimate depends at most upon $ε, r$ and the degree of the hypersurface.36 pages; appendix by J. StarrNumber TheoryAlgebraic Geometry11D45 (11G35,14G05)text