Generating class fields using Shimura reciprocity

  • Alice Gee
  • Peter Stevenhagen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1423)


The abelian extensions of an imaginary quadratic field can theoretically be generated by the values of the modular j-function, but these values are too large to be useful in practice. We show how Shimura's reciprocity law can be applied to find small generators for these extensions, and to compute the corresponding irreducible polynomials.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Alice Gee
    • 1
  • Peter Stevenhagen
    • 1
  1. 1.Universiteit van AmsterdamTV AmsterdamThe Netherlands

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