Computation of the class number and class group of a complex cubic field

Authors:
G. Dueck and H. C. Williams

Journal:
Math. Comp. **45** (1985), 223-231

MSC:
Primary 11R16; Secondary 11R29, 11Y40

DOI:
https://doi.org/10.1090/S0025-5718-1985-0790655-4

Corrigendum:
Math. Comp. **50** (1988), 655-657.

MathSciNet review:
790655

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Abstract: Let *h* and *G* be, respectively, the class number and the class group of a complex cubic field of discriminant . A method is described which makes use of recent ideas of Lenstra and Schoof to develop fast algorithms for finding *h* and *G*. Under certain Riemann hypotheses it is shown that these algorithms will compute *h* in elementary operations and *G* in elementary operations. Finally, the results of running some computer programs to determine *h* and *G* for all pure cubic fields , with , are summarized.

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DOI:
https://doi.org/10.1090/S0025-5718-1985-0790655-4

Article copyright:
© Copyright 1985
American Mathematical Society