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Lattice Points
Quadratic Form
Symmetric Space
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Strong wavefront lemma and counting lattice points in sectors
Strong wavefront lemma and counting lattice points in sectors,10.1007/s1185601000358,Israel Journal of Mathematics,Alexander Gorodnik,Hee Oh,Nimish
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Strong wavefront lemma and counting lattice points in sectors
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Citations: 4
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Alexander Gorodnik
,
Hee Oh
,
Nimish Shah
We compute the asymptotics of the number of integral quadratic forms with prescribed orthogonal decompositions and more generally, the asymptotics of the number of
lattice points
lying in sectors of affine symmetric spaces. A new key ingredient in this article is the strong wavefront lemma, which shows that the generalized Cartan decomposition associated to a
symmetric space
is uniformly Lipschitz.
Journal:
Israel Journal of Mathematics  ISR J MATH
, vol. 176, no. 1, pp. 419444, 2010
DOI:
10.1007/s1185601000358
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References
(9)
Upper bounds and asymptotics in a quantitative version of the Oppenheim conjecture
(
Citations: 45
)
A. Eskin
,
G. A. Margulis
,
S. Mozes
Published in 1998.
Orbits of discrete subgroups on a symmetric space and the Furstenberg boundary
(
Citations: 9
)
Alexander Gorodnik
,
Hee Oh
Journal:
Duke Mathematical Journal  DUKE MATH J
, vol. 139, no. 2007, pp. 483525, 2007
Density of integer points on affine homogeneous varieties
(
Citations: 44
)
W. Duke
,
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Journal:
Duke Mathematical Journal  DUKE MATH J
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Mixing, counting, and equidistribution in Lie groups
(
Citations: 91
)
Alex Eskin
,
Curt McMullen
Journal:
Duke Mathematical Journal  DUKE MATH J
, vol. 71, no. 1993, pp. 181209, 1993
Exponential volume growth, maximal functions on symmetric spaces, and ergodic theorems for semisimple Lie groups
(
Citations: 3
)
AMOS NEVO
Journal:
Ergodic Theory and Dynamical Systems  ERGOD THEOR DYN SYST
, vol. 25, no. 4, pp. 12571294, 2005
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Citations
(4)
The asymptotic distribution of circles in the orbits of Kleinian groups
(
Citations: 2
)
Hee Oh
,
Nimish Shah
Journal:
Inventiones Mathematicae  INVENT MATH
, vol. 187, no. 1, pp. 13, pp. 135, 2012
Equidistribution and Counting for orbits of geometrically finite hyperbolic groups
Hee Oh
,
Nimish Shah
Published in 2012.
Counting visible circles on the sphere and Kleinian groups
(
Citations: 1
)
Hee Oh
,
Nimish Shah
Published in 2010.
On the distribution of orbits of geometrically finite hyperbolic groups on the boundary (with appendix by Francois Maucourant)
Seonhee Lim
,
Hee Oh
Published in 2010.