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

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dc.creatorGorodnik, Alexander
dc.date2003-10-16
dc.date.accessioned2026-07-07T05:01:56Z
dc.date.available2026-07-07T05:01:56Z
dc.descriptionLet 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\in 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.
dc.descriptionTo be published in Trans. Amer. Math. Soc., 17 pages
dc.identifierhttps://arxiv.org/abs/math/0310231
dc.identifierhttp://arxiv.org/abs/math/0310231
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68867
dc.subjectDynamical Systems
dc.subjectNumber Theory
dc.subject37A17, 11J13, 11H55
dc.titleOppenheim conjecture for pairs consisting of a linear form and a quadratic form
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