2005/05/10 by Browning, T. D., Heath-Brown, D. R.
#11D45 (11G35 #14G05) #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.math/0505186
This paper establishes the conjecture that a non-singular projective hypersurface of dimension r, which is not equal to a linear space, contains O(Br+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.