Integral points on cubic hypersurfaces

2006/11/03 by TD Browning, Heath-Brown, Browning, T. D. +1 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Meromorphic and Entire Functions #Advanced Differential Equations and Dynamical Systems

paper · pdf · doi:10.48550/arxiv.math/0611086

Abstract

Let g be a cubic polynomial with integer coefficients and n>9 variables, and assume that the congruence g=0 modulo p^k is soluble for all prime powers p^k. We show that the equation g=0 has infinitely many integer solutions when the cubic part of g defines a projective hypersurface with singular locus of dimension

Citations

• On the number of points on a complete intersection over a finite field

Cited by

• Counting rational points on cubic hypersurfaces

Related

• Counting rational points on cubic hypersurfaces
• How often does a cubic hypersurface have a rational point?
• Quadratic congruences on average and rational points on cubic surfaces
• Diophantine equations in primes: density of prime points on affine hypersurfaces
• Inhomogeneous cubic congruences and rational points on del Pezzo surfaces