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Voronoi’s algorithm in purely cubic congruence function fields of unit rank 1. (English) Zbl 1042.11068
Summary: 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.

11R16 Cubic and quartic extensions
11R27 Units and factorization
11R58 Arithmetic theory of algebraic function fields
11-04 Software, source code, etc. for problems pertaining to number theory
Full Text: DOI
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