Advanced Search
Article Contents
Article Contents

A quantitative Oppenheim theorem for generic ternary quadratic forms

AG: Partially supported by ISF-UGC. DK: Partially supported by NSF grant DMS-1401747.
Abstract Full Text(HTML) Related Papers Cited by
  • We prove a quantitative version of Oppenheim's conjecture for generic ternary indefinite quadratic forms. Our results are inspired by and analogous to recent results for diagonal quadratic forms due to Bourgain [3].

    Mathematics Subject Classification: Primary: 11E20; Secondary: 37A17.


    \begin{equation} \\ \end{equation}
  • 加载中
  • [1] J. S. Athreya and G. A. Margulis, Logarithm laws for unipotent flows. I, J. Mod. Dyn., 3 (2009), 359-378.  doi: 10.3934/jmd.2009.3.359.
    [2] J. S. Athreya and G. A. Margulis, Values of random polynomials at integer points, J. Mod. Dyn. , to appear.
    [3] J. Bourgain, A quantitative Oppenheim theorem for generic diagonal quadratic forms, Israel J. Math., 215 (2016), 503-512.  doi: 10.1007/s11856-016-1385-7.
    [4] S. G. Dani and G. A. Margulis, Limit distributions of orbits of unipotent flows and values of quadratic forms, Adv. in Soviet Math., 16 (1993), 91-137. 
    [5] A. EskinG. Margulis and S. Mozes, Upper bounds and asymptotics in a quantitative version of the Oppenheim conjecture, Ann. of Math. (2), 147 (1998), 93-141.  doi: 10.2307/120984.
    [6] A. Ghosh, A. Gorodnik and A. Nevo, Best possible rates of distribution of dense lattice orbits in homogeneous spaces, J. Reine Angew. Math. , to appear.
    [7] A. Ghosh, A. Gorodnik and A. Nevo, Optimal density for values of generic polynomial maps, arXiv:1801.01027, 2018.
    [8] A. Ghosh and D. Kelmer, Shrinking targets for semisimple groups, Bull. Lond. Math. Soc., 49 (2017), 235-245.  doi: 10.1112/blms.12023.
    [9] A. Gorodnik and A. Nevo, The Ergodic Theory of Lattice Subgroups, Annals of Mathematics Studies, 172, Princeton University Press, Princeton, NJ, 2010.
    [10] E. Lindenstrauss and G. Margulis, Effective estimates on indefinite ternary forms, Israel J. Math., 203 (2014), 445-499.  doi: 10.1007/s11856-014-1110-3.
    [11] G. A. Margulis, Discrete subgroups and ergodic theory, in Number Theory, Trace Formulas and Discrete Groups (Oslo, 1987), Academic Press, Boston, MA, 1989,377-398.
    [12] H. Oh, Tempered subgroups and representations with minimal decay of matrix coefficients, Bull. Soc. Math. France, 126 (1998), 355-380.  doi: 10.24033/bsmf.2329.
    [13] C. A. Rogers, Mean values over the space of lattices, Acta Math., 94 (1955), 249-287.  doi: 10.1007/BF02392493.
    [14] P. Sarnak, Values at integers of binary quadratic forms, in Harmonic Analysis and Number Theory (Montreal, PQ, 1996), CMS Conf. Proc., 21, AMS, Providence, RI, (1997), 181-203.
  • 加载中

Article Metrics

HTML views(1695) PDF downloads(250) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint