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Voronoi's Algorithm in Purely Cubic Congruence Function Fields of Unit Rank 1

R. Scheidler and A. Stein
Mathematics of Computation
Vol. 69, No. 231 (Jul., 2000), pp. 1245-1266
Stable URL: http://www.jstor.org/stable/2585026
Page Count: 22
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Voronoi's Algorithm in Purely Cubic Congruence Function Fields of Unit Rank 1
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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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