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Tame kernels of cubic cyclic fields

Author: Jerzy Browkin
Journal: Math. Comp. 74 (2005), 967-999
MSC (2000): Primary 11R70; Secondary 11R16, 11Y40, 19--04, 19C99
Published electronically: October 27, 2004
MathSciNet review: 2114659
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Abstract: There are many results describing the structure of the tame kernels of algebraic number fields and relating them to the class numbers of appropriate fields. In the present paper we give some explicit results on tame kernels of cubic cyclic fields. Table 1 collects the results of computations of the structure of the tame kernel for all cubic fields with only one ramified prime $p,$ $7\le p<5,000.$

In particular, we investigate the structure of the 7-primary and 13-primary parts of the tame kernels. The theoretical tools we develop, based on reflection theorems and singular primary units, enable the determination of the structure even of 7-primary and 13-primary parts of the tame kernels for all fields as above. The results are given in Tables 2 and 3.

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Additional Information

Jerzy Browkin
Affiliation: Institute of Mathematics, University of Warsaw, ul. Banacha 2, PL–02–097 Warsaw, Poland

Keywords: Cubic fields, cyclic fields, tame kernel
Received by editor(s): October 17, 2002
Received by editor(s) in revised form: May 4, 2004
Published electronically: October 27, 2004
Article copyright: © Copyright 2004 American Mathematical Society