Distribution of lattice orbits on homogeneous varieties

Details Distribution of lattice orbits on homogeneous varieties Distribution of lattice orbits on homogeneous varieties

2004-07-20

arxiv.org/abs/math/0407345v1

Mathematics

Dynamical Systems

Scientific paper

Given a lattice \Gamma in a locally compact group G and a closed subgroup H of G, one has a natural action of \Gamma on the homogeneous space V=H\G. For an increasing family of finite subsets {\Gamma_T: T>0}, a dense orbit v\Gamma, v\in V, and compactly supported function \phi on V, we consider the sums S_{\phi,v}(T)=\sum_{\gamma\in \Gamma_T} \phi(v \gamma). Understanding the asymptotic behavior of S_{\phi,v}(T) is a delicate problem which has only been considered for certain very special choices of H, G and {\Gamma_T}. We develop a general abstract approach to the problem, and apply it to the case when G is a Lie group and either H or G is semisimple. When G is a group of matrices equipped with a norm, we have S_{\phi,v}(T) \sim \int_{G_T} \phi(vg) dg, where G_T={g\in G:||g||

Affiliated with

Also associated with

No associations

Rating

Distribution of lattice orbits on homogeneous varieties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Distribution of lattice orbits on homogeneous varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Distribution of lattice orbits on homogeneous varieties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-143373