Computing class fields via the Artin map

Fieker, Claus

doi:10.1090/S0025-5718-00-01255-2

Computing class fields via the Artin map

Author: Claus Fieker
Journal: Math. Comp. 70 (2001), 1293-1303
MSC (2000): Primary 11Y40; Secondary 11R37
DOI: https://doi.org/10.1090/S0025-5718-00-01255-2
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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