Geodesic
Matrix coefficients, counting and primes for orbits of geometrically finite groups
Journal of the European Mathematical Society, Tome 17 (2015) no. 4, pp. 837-897

Voir la notice de l'article provenant de la source EMS Press

Let G:=SO(n,1)∘ and Γa geometrically finite Zariski dense subgroup with critical exponent δ bigger than (n−1)/2. Under a spectral gap hypothesis on L2(Γ\G), which is always satisfied when δ>(n−1)/2 for n=2,3 and when δ>n−2 for n≥4, we obtain an effective archimedean counting result for a discrete orbit of Γ in a homogeneous space H\G where H is the trivial group, a symmetric subgroup or a horospherical subgroup. More precisely, we show that for any effectively well-rounded family {BT​⊂H\G} of compact subsets, there exists η>0 such that
DOI : 10.4171/jems/520
Classification : 11-XX, 18-XX, 19-XX, 34-XX
Keywords: Geometrically finite group, matrix coefficients, mixing, sieve, spectral gap, equidistribution 
@article{JEMS_2015_17_4_a5,
     author = {Amir Mohammadi and Hee Oh},
     title = {Matrix coefficients, counting and primes for orbits of geometrically finite groups},
     journal = {Journal of the European Mathematical Society},
     pages = {837--897},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {2015},
     doi = {10.4171/jems/520},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/520/}
}
TY  - JOUR
AU  - Amir Mohammadi
AU  - Hee Oh
TI  - Matrix coefficients, counting and primes for orbits of geometrically finite groups
JO  - Journal of the European Mathematical Society
PY  - 2015
SP  - 837
EP  - 897
VL  - 17
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/520/
DO  - 10.4171/jems/520
ID  - JEMS_2015_17_4_a5
ER  - 
%0 Journal Article
%A Amir Mohammadi
%A Hee Oh
%T Matrix coefficients, counting and primes for orbits of geometrically finite groups
%J Journal of the European Mathematical Society
%D 2015
%P 837-897
%V 17
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/520/
%R 10.4171/jems/520
%F JEMS_2015_17_4_a5
Amir Mohammadi; Hee Oh. Matrix coefficients, counting and primes for orbits of geometrically finite groups. Journal of the European Mathematical Society, Tome 17 (2015) no. 4, pp. 837-897. doi: 10.4171/jems/520

Cité par Sources :