Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Matrix coefficients, Counting and Primes for orbits of geometrically
  finite groups   Let G:=SO(n,1)^\circ and \Gamma be a geometrically finite Zariski dense
subgroup with critical exponent delta bigger than (n-1)/2. Under a spectral gap
hypothesis on L^2(\Gamma \ G), which is always satisfied for delta>(n-1)/2 for
n=2,3 and for delta>n-2 for n>= 4, we obtain an {\it effective} archimedean
counting result for a discrete orbit of \Gamma in a homogeneous space H\G,
where H is the trivial group, an affine symmetric subgroup or a horospherical
subgroup. More precisely, we show that for any effectively well-rounded family
{B_T} of compact subsets in H\G, there exists \eta>0 such that #[e]\G\cap
B_T=M(B_T) +O(M(B_T)^{1-\eta}) for an explicit measure M on H\G, which depends
on Gamma. We also apply affine sieve and describe the distribution of almost
primes on orbits of \Gamma in arithmetic settings.
  One of key ingredients in our approach is an effective asymptotic formula for
the matrix coefficients of L^2(\Gamma \ G) that we prove by combining methods
from spectral analysis, harmonic analysis and ergodic theory. An effective
mixing for the Bowen-Margulis-Sullivan measure is also obtained as an
application of our methods.

28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin