Counting rational points on hypersurfaces

2004/04/26 by T. D. Browning, D. R. Heath‐Brown, D. R. Heath-Brown +2 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #math.NT #msc:11G35

paper · pdf · doi:10.48550/arxiv.math/0404456

30 pages

arxiv created 2005/03/18 · arxiv updated 2009/12/01

Abstract

Let F(x₁,...,x_n) be a form of degree d≥ 2, which produces a geometrically irreducible hypersurface in 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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• Counting rational points on cubic hypersurfaces

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