Skip to main content
SpringerLink
Log in

Integral spinor norms in dyadic local fields III

  • Articles
  • Published:
Science China Mathematics Aims and scope Submit manuscript

Abstract

In this paper we give an alternative computation of integral spinor norms over dyadic local fields by using the Jordan decomposition of W-type. In particular, we emphasize the striking similarity between the theory over dyadic local fields and that over the local fields of characteristic 2.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Beli C N. Integral spinor norm groups over dyadic local fields. J Number Theory, 2003, 102: 125–182

    Article  MATH  MathSciNet  Google Scholar 

  2. Earnest A G, Hsia J S. Spinor norms of local integral rotations II. Pacific J Math, 1975, 61: 71–86; errata, 1984, 115: 493–494

    MATH  MathSciNet  Google Scholar 

  3. Eichler M. Die Ähnlichkeitsklassen indefiniter Gitter. Math Z, 1952, 55: 216–252

    Article  MATH  MathSciNet  Google Scholar 

  4. Hsia J S. Spinor norms of local integral rotations I. Pacific J Math, 1975, 57: 199–206

    MATH  MathSciNet  Google Scholar 

  5. Kneser M. Klassenzahlen indefiniter quadratischer Formen in drei oder mehr Veränderlichen. Arch Math, 1956, 7: 323–332

    Article  MATH  MathSciNet  Google Scholar 

  6. Lü J R. Integral spinor norms and relative spinor norms over dyadic local fields. PhD Thesis. Beijing: Academy of Mathematics and System Science, Chinese Academy of Sciences, 2010

    Google Scholar 

  7. O’Meara O T. Introduction to Quadratic Forms. Berlin: Springer, 1963

    MATH  Google Scholar 

  8. Riehm C R. On the integral representations of quadratic forms over local fields. Amer J Math, 1964, 86: 25–62

    Article  MATH  MathSciNet  Google Scholar 

  9. Riehm C R. Integral representations of quadratic forms in characteristic 2. Amer J Math, 1965, 87: 32–64

    Article  MATH  MathSciNet  Google Scholar 

  10. Sah C H. Quadratic forms over fields of characteristic 2. Amer J Math, 1960, 82: 812–830.

    Article  MATH  MathSciNet  Google Scholar 

  11. Wang Y, Xu F. Spinor genera in characteristic 2. Mem Amer Math Soc, 2008, 194: 1–83

    Google Scholar 

  12. Xu F. A remark on spinor norms of local integral rotations I. Pacific J Math, 1989, 136: 81–84

    MATH  MathSciNet  Google Scholar 

  13. Xu F. Integral spinor norms in dyadic local fields I. Pacific J Math, 1993, 157: 179–200

    MATH  MathSciNet  Google Scholar 

  14. Xu F. Generation of integral orthogonal groups over dyadic local fields. Pacific J Math, 1995, 167: 385–398

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Jinan University, Guangzhou, 510632, China

    JianRui Lü

  2. School of Mathematics, Capital Normal University, Beijing, 100048, China

    Fei Xu

Authors
  1. JianRui Lü
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fei Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fei Xu.

Additional information

Dedicated to Professor Wang Yuan on the Occasion of his 80th Birthday

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lü, J., Xu, F. Integral spinor norms in dyadic local fields III. Sci. China Math. 53, 2425–2446 (2010). https://doi.org/10.1007/s11425-010-4084-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-010-4084-6

Keywords

MSC(2000)

Search

Navigation