Integral points on cubic hypersurfaces
Number Theory
2007-06-19 v2 Algebraic Geometry
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 <n-10. The proof is based on the Hardy-Littlewood circle method.
Cite
@article{arxiv.math/0611086,
title = {Integral points on cubic hypersurfaces},
author = {T. D. Browning and D. R. Heath-Brown},
journal= {arXiv preprint arXiv:math/0611086},
year = {2007}
}
Comments
18 pages