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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.<\/p>","DOI":"10.1090\/s0025-5718-00-01255-2","type":"journal-article","created":{"date-parts":[[2002,11,6]],"date-time":"2002-11-06T14:02:22Z","timestamp":1036591342000},"page":"1293-1303","source":"Crossref","is-referenced-by-count":26,"title":["Computing class fields via the Artin map"],"prefix":"10.1090","volume":"70","author":[{"given":"Claus","family":"Fieker","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2000,3,24]]},"reference":[{"issue":"227","key":"1","doi-asserted-by":"publisher","first-page":"1179","DOI":"10.1090\/S0025-5718-99-01084-4","article-title":"Computing automorphisms of abelian number fields","volume":"68","author":"Acciaro, Vincenzo","year":"1999","journal-title":"Math. 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