Oppenheim Conjecture for Pairs Consisting of a Linear Form and a Quadratic Form
نویسنده
چکیده
Let Q be a nondegenerate quadratic form, and L is 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 ∈ Z} is dense in R provided that Q and L satisfy some natural conditions. The proof uses dynamics on homogeneous spaces of Lie groups.
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