Citation: |
[1] |
V. Bernik, D. Kleinbock and G. A. Margulis, Khintchine-type theorems on manifolds: the convergence case for standard and multiplicative versions, Internat. Math. Res. Notices, (2001), 453-486.doi: 10.1155/S1073792801000241. |
[2] |
A. Borel and J. Tits, Groupes réductifs, Inst. Hautes Études Sci. Publ. Math., 27 (1965), 55-150. |
[3] |
S. G. Dani, Invariant measures of horospherical flows on noncompact homogeneous spaces, Invent. Math., 47 (1978), 101-138.doi: 10.1007/BF01578067. |
[4] |
W. Duke, Z. Rudnick and P. Sarnak, Density of integer points on affine homogeneous varieties, Duke Math. J., 71 (1993), 143-179.doi: 10.1215/S0012-7094-93-07107-4. |
[5] |
A. Eskin and C. McMullen, Mixing, counting, and equidistribution in Lie groups, Duke Math. J., 71 (1993), 181-209.doi: 10.1215/S0012-7094-93-07108-6. |
[6] |
J. Franke, Y. I. Manin and Y. Tschinkel, Rational points of bounded height on Fano varieties, Invent. Math., 95 (1989), 421-435.doi: 10.1007/BF01393904. |
[7] |
J. E. Humphreys, Linear Algebraic Groups, Graduate Texts in Mathematics, 21, Springer-Verlag, New York-Heidelberg, 1975. |
[8] |
D. Y. Kleinbock and G. A. Margulis, Flows on homogeneous spaces and Diophantine approximation on manifolds, Ann. of Math. (2), 148 (1998), 339-360.doi: 10.2307/120997. |
[9] |
D. Y. Kleinbock and G. A. Margulis, On effective equidistribution of expanding translates of certain orbits in the space of lattices, in Number Theory, Analysis and Geometry, Springer, New York, 2012, 385-396.doi: 10.1007/978-1-4614-1260-1_18. |
[10] |
D. Kleinbock, R. Shi and B. Weiss, Pointwise equidistribution with an error rate and with respect to unbounded functions, arXiv:1505.06717, 2015. |
[11] |
D. Kleinbock and B. Weiss, Dirichlet's theorem on Diophantine approximation and homogeneous flows, J. Mod. Dyn., 2 (2008), 43-62. |
[12] |
G. A. Margulis, On some aspects of the theory of Anosov systems, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2004.doi: 10.1007/978-3-662-09070-1. |
[13] |
A. Mohammadi and A. S. Golsefidy, Translate of horospheres and counting problems, Amer. J. Math., 136 (2014), 1301-1346.doi: 10.1353/ajm.2014.0037. |
[14] |
H. Oh, Orbital counting via mixing and unipotent flows, in Homogeneous Flows, Moduli Spaces and Arithmetic, Clay Math. Proc., 10, Amer. Math. Soc., Providence, RI, 2010, 339-375. |
[15] |
P. Sarnak, Asymptotic behavior of periodic orbits of the horocycle flow and Eisenstein series, Comm. Pure Appl. Math., 34 (1981), 719-739.doi: 10.1002/cpa.3160340602. |
[16] |
A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. (N.S.), 20 (1956), 47-87. |
[17] |
N. Shah and B. Weiss, On actions of epimorphic subgroups on homogeneous spaces, Ergodic Theory Dynam. Systems, 20 (2000), 567-592.doi: 10.1017/S0143385700000298. |
[18] |
N. A. Shah, Limit distributions of expanding translates of certain orbits on homogeneous spaces, Proc. Indian Acad. Sci. Math. Sci., 106 (1996), 105-125.doi: 10.1007/BF02837164. |
[19] |
R. Shi, Expanding cone and applications to homogeneous dynamics, arXiv:1510.05256, 2015. |
[20] |
D. Zagier, Eisenstein series and the Riemann zeta-function, in Automorphic Forms, Representation Theory and Arithmetic, Tata Inst. Fund. Res. Studies in Math., 10, Tata Inst. Fundamental Res., Bombay, 275-301, 1981. |