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Oppenheim conjecture for pairs consisting of a linear form and a quadratic form

Authors:	Alexander Gorodnik

Institution:	Department of Mathematics, Ohio State University, Columbus, Ohio 43210

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

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