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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Computing class fields via the Artin map


Author: Claus Fieker
Journal: Math. Comp. 70 (2001), 1293-1303
MSC (2000): Primary 11Y40; Secondary 11R37
Published electronically: March 24, 2000
MathSciNet review: 1826583
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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.


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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

DOI: http://dx.doi.org/10.1090/S0025-5718-00-01255-2
PII: S 0025-5718(00)01255-2
Keywords: Computational algebraic number theory, class field theory, Artin reciprocity
Received by editor(s): April 6, 1999
Received by editor(s) in revised form: August 16, 1999
Published electronically: March 24, 2000
Article copyright: © Copyright 2000 American Mathematical Society