Skip to main content

Experimental results on class groups of real quadratic fields

Extended abstract

  • Conference paper
  • First Online:
Algorithmic Number Theory (ANTS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1423))

Included in the following conference series:

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E. Bach. Explicit bounds for primality testing and related problems. Math. Comp., 55(191):355–380, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  2. J. Buchmann, M.J. Jacobson, Jr., and E. Teske. On some computational problems in finite abelian groups. Math. Comp., 66(220): 1663–1687, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  3. D.A. Buell. Small class numbers and extreme values of L-functions of quadratic fields. Math. Comp., 31(139):786–796, 1977.

    Article  MATH  MathSciNet  Google Scholar 

  4. D.A. Buell. The last exhaustive computation of class groups of complex quadratic number fields. To appear in Number Theory: Fifth Conference of the Canadian Number Theory Association, 1996.

    Google Scholar 

  5. H. Cohen. A Course in Computational Algebraic Number Theory. Springer-Verlag, Berlin, 1993.

    Google Scholar 

  6. H. Cohen and H.W. Lenstra, Jr. Heuristics on class groups of number fields. In Number Theory, Lecture notes in Math., volume 1068, pages 33–62. Springer-Verlag, New York, 1983.

    Google Scholar 

  7. H. Cohen and H.W. Lenstra, Jr. Heuristics on class groups. In Number Theory (Noordwijkerhout, 1983), Lecture Notes in Math., volume 1052, pages 26–36. Springer-Verlag, New York, 1984.

    Google Scholar 

  8. A. Geist, A. Beguelin, J. Dongarra, W. Jiang, R. Manchek, and V. Sunderam. PVM: Parallel Virtual Machine — A User's Guide and Tutorial for Networked Parallel Computing. MIT Press, Cambridge, Mass., 1994.

    Google Scholar 

  9. C. Hooley. On the Pellian equation and the class number of indefinite binary quadratic forms. J. reine angew. Math., 353:98–131, 1984.

    MATH  MathSciNet  Google Scholar 

  10. M.J. Jacobson, Jr., R.F. Lukes, and H.C. Williams. An investigation of bounds for the regulator of quadratic fields. Experimental Mathematics, 4(3):211–225, 1995.

    MATH  MathSciNet  Google Scholar 

  11. D.H. Lehmer, E. Lehmer, and D. Shanks. Integer sequences having prescribed quadratic character. Math. Comp., 24(110):433–451, 1970.

    Article  MATH  MathSciNet  Google Scholar 

  12. LiDIA. http://www.informatik.tu-darmstadt.de/TI/LiDIA, 1997.

    Google Scholar 

  13. J.E. Littlewood. On the class number of the corpus P(√−k). Proc. London Math. Soc., 27:358–372, 1928.

    MATH  MathSciNet  Google Scholar 

  14. D. Shanks. Systematic examination of Littlewood's bounds on L(1, χ In Proc. Sympos. Pure Math, pages 267–283. AMS, Providence, R.I., 1973.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Joe P. Buhler

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jacobson, M.J. (1998). Experimental results on class groups of real quadratic fields. In: Buhler, J.P. (eds) Algorithmic Number Theory. ANTS 1998. Lecture Notes in Computer Science, vol 1423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054885

Download citation

  • DOI: https://doi.org/10.1007/BFb0054885

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64657-0

  • Online ISBN: 978-3-540-69113-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics