Voronoi’s algorithm in purely cubic congruence function fields of unit rank 1
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- by R. Scheidler and A. Stein PDF
- Math. Comp. 69 (2000), 1245-1266 Request permission
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.References
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Additional Information
- R. Scheidler
- Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, DE 19716
- MR Author ID: 308756
- ORCID: 0000-0001-7164-8769
- Email: scheidle@math.udel.edu
- A. Stein
- Affiliation: Department of Combinatorics & Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1, CANADA
- Email: astein@cacr.math.uwaterloo.ca
- 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.
- © Copyright 2000 American Mathematical Society
- Journal: Math. Comp. 69 (2000), 1245-1266
- MSC (1991): Primary 11R16, 11R27; Secondary 11R58, 11-04
- DOI: https://doi.org/10.1090/S0025-5718-99-01136-9
- MathSciNet review: 1653974