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Voronoi's algorithm
in purely cubic congruence function fields
of unit rank 1

Authors: R. Scheidler and A. Stein
Journal: Math. Comp. 69 (2000), 1245-1266
MSC (1991): Primary 11R16, 11R27; Secondary 11R58, 11-04
Published electronically: March 11, 1999
MathSciNet review: 1653974
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Abstract: The first part of this paper classifies all purely cubic function fields over a finite field of characteristic not equal to 3. In the remainder, we describe a method for computing the fundamental unit and regulator of a purely cubic congruence function field of unit rank 1 and characteristic at least 5. The technique is based on Voronoi's algorithm for generating a chain of successive minima in a multiplicative cubic lattice, which is used for calculating the fundamental unit and regulator of a purely cubic number field.

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Additional Information

R. Scheidler
Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, DE 19716

A. Stein
Affiliation: Department of Combinatorics & Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1, CANADA

Keywords: Purely cubic function field, Voronoi's algorithm, minimum, reduced ideal, fundamental unit, regulator
Received by editor(s): March 31, 1998
Received by editor(s) in revised form: August 14, 1998
Published electronically: March 11, 1999
Additional Notes: The first author was supported by NSF grant DMS-9631647.
Article copyright: © Copyright 2000 American Mathematical Society