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Mathematics of Computation

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Computing all power integral bases in orders of
totally real cyclic sextic number fields

Author: István Gaál
Journal: Math. Comp. 65 (1996), 801-822
MSC (1991): Primary 11Y50; Secondary 11Y40, 11D57
MathSciNet review: 1333313
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Abstract: An algorithm is given for determining all power integral bases in orders of totally real cyclic sextic number fields. The orders considered are in most cases the maximal orders of the fields. The corresponding index form equation is reduced to a relative Thue equation of degree 3 over the quadratic subfield and to some inhomogeneous Thue equations of degree 3 over the rationals. At the end of the paper, numerical examples are given.

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Additional Information

István Gaál
Affiliation: Kossuth Lajos University, Mathematical Institute, H–4010 Debrecen Pf.12., Hungary

Keywords: Cyclic sextic number fields, index form equation, power bases
Received by editor(s): May 2, 1994
Received by editor(s) in revised form: March 7, 1995
Additional Notes: This work was begun during the author’s stay in Düsseldorf as a fellow of the Alexander von Humboldt Foundation and completed under the partial support of the Hungarian National Foundation for Scientific research Grant no. 1641/91.
Article copyright: © Copyright 1996 American Mathematical Society