#### Filter Results:

#### Publication Year

2006

2016

#### Publication Type

#### Co-author

#### Publication Venue

Learn More

We prove mean and pointwise ergodic theorems for general families of averages on a semisimple algebraic (or S-algebraic) group G, together with an explicit rate of convergence when the action has a spectral gap. Given any lattice Γ in G, we use the ergodic theorems for G to solve the lattice point counting problem for general domains in G, and prove mean… (More)

For a locally compact second countable group G and a lattice subgroup Γ, we give an explicit quantitative solution of the lattice point counting problem in general domains in G, provided that i) G has finite upper local dimension, and the domains satisfy a basic regularity condition, ii) the mean ergodic theorem for the action of G on G/Γ holds, with a rate… (More)

- Amos Nevo, Peter Sarnak
- 2009

We develop the affine sieve in the context of orbits of congruence subgroups of semi-simple groups acting linearly on affine space. In particular we give effective bounds for the saturation numbers for points on such orbits at which the value of a given polynomial has few prime factors. In many cases these bounds are of the same quality as what is known in… (More)

Let 0 denote a word-hyperbolic group, and let S = S 01 denote a nite symmetric set of generators. Let S n = fw : jwj = ng denote the sphere of radius n, where j1j denotes the word length on 0 induced by S. Dene n d = 1 #S n P w2S n w, and n = 1 n+1 P n k=0 k. Let (X; B; m) be a probability space on which 0 acts ergodically by measure preserving… (More)

We consider actions of non-compact simple Lie groups preserving an analytic rigid geometric structure of algebraic type on a compact manifold. The structure is not assumed to be uni-modular, so an invariant measure may not exist. Ergodic stationary measures always exist, and when such a measure has full support, we show the following. 1) Either the manifold… (More)

- Amos Nevo, Peter Sarnak
- 2008

We develop the affine sieve in the context of orbits of congruence subgroups of semi-simple groups acting linearly on affine space. In particular we give effective bounds for the saturation numbers for points on such orbits at which the value of a given polynomial has few prime factors. In many cases these bounds are of the same quality as what is known in… (More)

- ‹
- 1
- ›