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

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

2003-10-16

arxiv.org/abs/math/0310231v1

Mathematics

Dynamical Systems

To be published in Trans. Amer. Math. Soc., 17 pages

Scientific paper

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.

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