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Generating class fields using Shimura reciprocity

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Book cover Algorithmic Number Theory (ANTS 1998)

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

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Abstract

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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Authors and Affiliations

  1. Universiteit van Amsterdam, Plantage Muidergracht 24, 1018, TV Amsterdam, The Netherlands

    Alice Gee & Peter Stevenhagen

Authors
  1. Alice Gee
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  2. Peter Stevenhagen
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Joe P. Buhler

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© 1998 Springer-Verlag Berlin Heidelberg

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Gee, A., Stevenhagen, P. (1998). Generating class fields using Shimura reciprocity. 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/BFb0054883

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  • DOI: https://doi.org/10.1007/BFb0054883

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64657-0

  • Online ISBN: 978-3-540-69113-6

  • eBook Packages: Springer Book Archive

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