Oppenheim conjecture for pairs consisting of a linear form and a quadratic form
Dynamical Systems
2007-05-23 v1 Number Theory
Abstract
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.
Cite
@article{arxiv.math/0310231,
title = {Oppenheim conjecture for pairs consisting of a linear form and a quadratic form},
author = {Alexander Gorodnik},
journal= {arXiv preprint arXiv:math/0310231},
year = {2007}
}
Comments
To be published in Trans. Amer. Math. Soc., 17 pages