Mathematische Annalen

, Volume 332, Issue 1, pp 37–53 | Cite as

On representations of spinor genera II



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Borovoi, M., On representations of integers by indefinite quadratic forms. J. Number Theory 90, 281–293 (2001)Google Scholar
  2. 2.
    Borovoi, M., Rudnick, Z.: Hardy-Littlewood varieties and semi-simple groups Invent. Math. 111, 37–66 (1995)Google Scholar
  3. 3.
    Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices and Groups. Springer-Verlag, 1993Google Scholar
  4. 4.
    Chan, W.K., Xu, F.: On representations of spinor genera. Compositio Math. 140, 287–300 (2004)CrossRefGoogle Scholar
  5. 5.
    Duke, W., Schulze-Pillot, R.: Representations of integers by positive ternary quadratic forms and equidistribution of lattices points on ellisoids. Invent. Math. 99, 49–57 (1990)Google Scholar
  6. 6.
    Hsia, J.S.: Spinor norms of local integral rotations Pacific. J. Math. 57, 199–206 (1975)Google Scholar
  7. 7.
    Hsia, J.S.: Representations by spinor genera Pacific, J. Math. 63, 147–152 (1976)Google Scholar
  8. 8.
    Hsia, J.S., Shao, Y.Y., Xu, F.: Representations of indefinite quadratic forms J. reine und angew. Math. 494, 129–140 (1998)Google Scholar
  9. 9.
    Hsia, J.S., Shao, Y.Y., Xu, F.: Spinor norms of relative local integral rotations. PreprintGoogle Scholar
  10. 10.
    Jones, B.W., Watson, G.L.: On indefinite ternary quadratic forms Canad. J. Math. 8, 592–608 (1956)Google Scholar
  11. 11.
    Kneser, M.: Darstellungsmasse indefiniter quadratischer. Formen Math. Z. 77, 188–194 (1961)Google Scholar
  12. 12.
    O’Meara, O.T.: The integral representations of quadratic forms over local fields. Amer. J. Math. 80, 843–878 (1958)Google Scholar
  13. 13.
    O’Meara, O.T.: Introduction to quadratic forms. Springer-Verlag, 1973Google Scholar
  14. 14.
    Ono, K., Soundararajan, K.: Ramanujan’s ternary quadratic form. Invent. Math. 130, 415–454 (1997)CrossRefGoogle Scholar
  15. 15.
    Siegel, C.L.: Indefinite quadratische Formen und Funktionentheorie I, Math. Ann. 124, 17–54 (1951)Google Scholar
  16. 16.
    Schulze-Pillot, R.: Darstellung durch Spinorgeschlechter ternärer quadratischer Formen. J. Number Theory 12, 529–540 (1980)CrossRefGoogle Scholar
  17. 17.
    Schulze-Pillot, R.: Exceptional integers for genera of integral ternary positive definite quadratic forms. Duke Math. J. 102, 351–357 (2000)CrossRefGoogle Scholar
  18. 18.
    Schulze-Pillot, R., Xu, F.: Representations by spinor genera of ternary quadratic forms. Contemp. Math. 344, 323–337 (2004)Google Scholar
  19. 19.
    Wiles, A.: Twenty years of number theory Mathematics: frontiers and perspectives. Amer. Math. Soc. 2000, pp. 329–342Google Scholar
  20. 20.
    Xu, F.: Integral spinor norms in dyadic local fields II, Acta Arith. LXIII. 3, 223–232 (1993)Google Scholar
  21. 21.
    Xu, F.: Arithmetic Springer theorem on quadratic forms under field extensions of odd degree, Contemp. Math. 249, 175–197 (1999)Google Scholar
  22. 22.
    Xu, F.: Representations of indefinite ternary quadratic forms over number fields, Math. Z. 234, 115–144 (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Academy of Mathematics and System Sciences, Chinese Academy of SciencesBeijingP.R. China

Personalised recommendations