A survey of computational class field theory. (English) Zbl 0949.11063

This paper immediately preceded the author’s new definitive book on class field theory [Advanced topics in computational number theory, Graduate Texts in Mathematics. 193. Springer (2000)]. So it is essentially an extended abstract (or outline), which also highlights certain current topics in that book, e.g., Stark’s units [X. F. Roblot, C. R. Acad. Sci., Paris, Sér. I 323, 1165-1168 (1996; Zbl 0871.11080)] and complex multiplication [R. Schertz, J. Théor. Nombres Bordx. 9, 383-394 (1997; Zbl 0902.11047)].


11Y40 Algebraic number theory computations
11R37 Class field theory
11-02 Research exposition (monographs, survey articles) pertaining to number theory
11G15 Complex multiplication and moduli of abelian varieties
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