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Numerical Results on Class Groups of Imaginary Quadratic Fields

  • Michael J. JacobsonJr.
  • Shantha Ramachandran
  • Hugh C. Williams
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4076)

Abstract

Using techniques described in [3], we have computed the class number and class group structure of all imaginary quadratic fields with discriminant Δ for 0 < |Δ| < 1011. A novel verification algorithm based on the Eichler Selberg Trace Formula [15] was used to ensure that the correctness of our results does not rely on any unproved hypothesis. We present the results of our computations, and remark on specific evidence that was found pertaining to a number of heuristics. In particular, we present data which supports some of the Cohen-Lenstra heuristics [8], Littlewood’s bounds on L(1,χ) [14], and Bach’s bound on the maximum norm of the prime ideals required to generate the class group [1].

Keywords

Prime Ideal Class Group Class Number Cusp Form Congruence Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Michael J. JacobsonJr.
    • 1
  • Shantha Ramachandran
    • 1
  • Hugh C. Williams
    • 1
  1. 1.Department of Computer ScienceUniversity of CalgaryCalgary, AlbertaCanada

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