Oppenheim conjecture for pairs consisting of a linear form and a quadratic form
Abstract
Description
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\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 pages
To be published in Trans. Amer. Math. Soc., 17 pages