TY - CHAP
AB - 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.
AU - Browning, Timothy D
AU - Heath Brown, Roger
ID - 164
T2 - Analytic Number Theory: Essays in honour of Klaus Roth
TI - Integral points on cubic hypersurfaces
ER -