Computing class fields via the Artin map
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Abstract:
Based on an explicit representation of the Artin map for Kummer extensions, we present a method to compute arbitrary class fields. As in the proofs of the existence theorem, the problem is first reduced to the case where the field contains sufficiently many roots of unity. Using Kummer theory and an explicit version of the Artin reciprocity law we show how to compute class fields in this case. We conclude with several examples.References
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Additional Information
- Claus Fieker
- Affiliation: Fachbereich 3, Mathematik MA 8–1, Technische Universität Berlin, Straße des 17. Juni 136, D-10623 Berlin, F.R.G.
- Email: fieker@math.tu-berlin.de
- Received by editor(s): April 6, 1999
- Received by editor(s) in revised form: August 16, 1999
- Published electronically: March 24, 2000
- © Copyright 2000 American Mathematical Society
- Journal: Math. Comp. 70 (2001), 1293-1303
- MSC (2000): Primary 11Y40; Secondary 11R37
- DOI: https://doi.org/10.1090/S0025-5718-00-01255-2
- MathSciNet review: 1826583