Counting rational points on hypersurfaces

Details Counting rational points on hypersurfaces Counting rational points on hypersurfaces

2004-04-26

arxiv.org/abs/math/0404456v3

Mathematics

Number Theory

30 pages

Scientific paper

Let $F(x_1,...,x_n)$ be a form of degree $d\geq 2$, which produces a geometrically irreducible hypersurface in $\mathbb{P}^{n-1}$. This paper is concerned with the number of rational points on F=0 which have height at most $B$. Whenever $n<6$, or whenever the hypersurface is not a union of lines, we obtain estimates that are essentially best possible and that are uniform in $d$ and $n$.

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