Integral points on cubic hypersurfaces

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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.
18 pages

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Number Theory, Algebraic Geometry, 11D72; 11P55

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http://salesiana.dossiersoluciones.com/handle/123456789/131959

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0611086
 http://arxiv.org/abs/math/0611086

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arXiv