## Abstract

Let Q be a nondegenerate quadratic form and L a nonzero linear form of dimension d > 3. As a generalization of the Oppenheim conjecture, we prove that the set {(Q(x); L(x)) : x is an element of Z(d)} is dense in R-2 provided that Q and L satisfy some natural conditions. The proof uses dynamics on homogeneous spaces of Lie groups.

Translated title of the contribution | Oppenheim conjecture for pairs consisting of a linear form and a quadratic form |
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Original language | English |

Pages (from-to) | 4447 - 4463 |

Number of pages | 17 |

Journal | Transactions of the American Mathematical Society |

Volume | 356 (11) |

Publication status | Published - Nov 2004 |