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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68867Let 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.To be published in Trans. Amer. Math. Soc., 17 pagesDynamical SystemsNumber Theory37A17, 11J13, 11H55Oppenheim conjecture for pairs consisting of a linear form and a quadratic formtext