## 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

Translated title of the contribution | Integral points on cubic hypersurfaces |
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Original language | English |

Title of host publication | Analytic Number Theory: Essays in Honour of Klaus Roth |

Editors | WWL Chen, WT Gowers, H Halberstam, WM Schmidt, RC Vaughan |

Publisher | Cambridge University Press |

Volume | In Press |

ISBN (Print) | 9780521515382 |

Publication status | Accepted/In press - 2007 |