Computation of the fundamental units and the regulator of a cyclic cubic function field. (English) Zbl 1064.11082

The authors present algorithms based on Voronoi’s method for computing the fundamental units and the regulator of cyclic cubic function fields over a finite field of order \(q \equiv 1\bmod 3\). The paper also contains tables with the results of their calculations. For example, the regulators of about 50 fields with \(7\leq q\leq 911\) are listed.


11Y40 Algebraic number theory computations
11R58 Arithmetic theory of algebraic function fields
11R27 Units and factorization
11R16 Cubic and quartic extensions
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