Counting rational points on hypersurfaces
By Tim D Browning, Heath-Brown. 2004
71 citations recorded by the source corpus.
Abstract For any n ≧ 2, let F ∈ ℤ [ x 1, … , xn ] be a form of degree d≧ 2, which produces a geometrically irreducible hypersurface in ℙn–1. This paper is concerned with the number N(F;B) of rational points on F = 0 which have height at most B. For any ε > 0 we establish the estimate N(F; B) = O(B n− 2+ ε ), whenever either n ≦ 5 or the hypersurface is not a union of lines. Here the implied constant depends at most upon d, n and ε.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/46f3957a88faa663d06fe4a84b5fa33c9e20880e
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Cubic forms in 14 variables (2007, background): “For a proof, see (2.2) and Lemma 4 of Browning and Heath-Brown [ 3 ], for example.”