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math.DS2003
Uniform distribution of orbits of lattices on spaces of frames
Alexander Gorodnik
We study distribution of orbits of a lattice Γ<SL(n,R) in the the space V_{n,l} of l-frames in R^n (1\le l\le n-1). Examples of dense Γ-orbits are known from the work of Dani, Ragh…
math.DS2003★ 2 cited
Lattice action on the boundary of SL(n,R)
Alexander Gorodnik
Let Γbe a lattice in G=SL(n,R) and X=G/S a homogeneous space of G, where S is a closed subgroup of G which contains a real algebraic subgroup H such that G/H is compact. We establi…
math.DS2003
Oppenheim conjecture for pairs consisting of a linear form and a quadratic form
Alexander Gorodnik
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…