Computation of the Class Number and Class Group of a Complex Cubic Field
نویسنده
چکیده
Let h and G be, respectively, the class number and the class group of a complex cubic field of discriminant A. 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 0(|A|1/5 + E) elementary operations and G in 0(|A|l/4 + F) elementary operations. Finally, the results of running some 3^ computer programs to determine h and G for all pure cubic fieldsâ(vD ), with 2 ^ D < 30,000, are summarized.
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تاریخ انتشار 2010