Counting rational points on quadric surfaces

Abstract

We give an upper bound for the number of rational points of height at most $B$, lying on a surface defined by a quadratic form $Q$. The bound shows an explicit dependence on $Q$. It is optimal with respect to $B$, and is also optimal for typical forms $Q$.

29 pages

Cited by in corpus (3)

• Density of rational points on a quadric bundle in ${\mathbb{P}}^3\times {\mathbb{P}}^3$
• Sums of four squareful numbers
• A uniform estimate for the density of rational points on quadrics