Uniform bounds for rational points on cubic hypersurfaces
Book chapter, 2015

© Cambridge University Press 2015. We use a global version of Heath-Brown’ p-adic determinant method to show that there are ON,ε(Bdim X + 1/7 + ε) rational points of height at most B on a geometrically integral variety X ⊂ PN of degree three defined over Q. By the same method we also show that there are Oε(B12/7 + ε) rational points of height at most B outside the lines on any cubic surface in P3.

Number Theory

Geometry and Topology

Author

Per Salberger

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Arithmetic and Geometry

401-421

Subject Categories

Mathematics

DOI

10.1017/CBO9781316106877.021

ISBN

9781316106877

More information

Created

10/7/2017