Experimental results on class groups of real quadratic fields

Extended abstract
  • Michael J. JacobsonJr.
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1423)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    E. Bach. Explicit bounds for primality testing and related problems. Math. Comp., 55(191):355–380, 1990.MATHMathSciNetCrossRefGoogle Scholar
  2. 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.MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    D.A. Buell. Small class numbers and extreme values of L-functions of quadratic fields. Math. Comp., 31(139):786–796, 1977.MATHMathSciNetCrossRefGoogle Scholar
  4. 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. 5.
    H. Cohen. A Course in Computational Algebraic Number Theory. Springer-Verlag, Berlin, 1993.Google Scholar
  6. 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. 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. 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. 9.
    C. Hooley. On the Pellian equation and the class number of indefinite binary quadratic forms. J. reine angew. Math., 353:98–131, 1984.MATHMathSciNetGoogle Scholar
  10. 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.MATHMathSciNetGoogle Scholar
  11. 11.
    D.H. Lehmer, E. Lehmer, and D. Shanks. Integer sequences having prescribed quadratic character. Math. Comp., 24(110):433–451, 1970.MATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    LiDIA., 1997.Google Scholar
  13. 13.
    J.E. Littlewood. On the class number of the corpus P(√−k). Proc. London Math. Soc., 27:358–372, 1928.MATHMathSciNetGoogle Scholar
  14. 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

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Michael J. JacobsonJr.
    • 1
  1. 1.FB Informatik, Institut für theoretische InformatikTechnische UniversitÄt DarmstadtDarmstadtGermany

Personalised recommendations