Computation of the fundamental units and the regulator of a cyclic cubic function field

Yoonjin Lee; Renate Scheidler; Christopher Yarrish

doi:10.1080/10586458.2003.10504493

Computation of the fundamental units and the regulator of a cyclic cubic function field

Yoonjin Lee, Renate Scheidler, Christopher Yarrish

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

This paper presents algorithms for computing the two fundamental units and the regulator of a cyclic cubic extension of a rational function field over a field of order q ≡ 1 (mod 3). The procedure is based on a method originally due to Voronoi that was recently adapted to purely cubic function fields of unit rank one. Our numerical examples show that the two fundamental units tend to have large degree, and frequently, the extension has a very small ideal class number.

Original language	English
Pages (from-to)	211-225
Number of pages	15
Journal	Experimental Mathematics
Volume	12
Issue number	2
DOIs	https://doi.org/10.1080/10586458.2003.10504493
State	Published - 2003

Bibliographical note

Funding Information:
Research of the second author was supported by NSA grant MSPF-OOIG-253.

Keywords

Fundamental unit
Minimum
Purely cubic function field
Reduced ideal
Regulator

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10.1080/10586458.2003.10504493

Cite this

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abstract = "This paper presents algorithms for computing the two fundamental units and the regulator of a cyclic cubic extension of a rational function field over a field of order q ≡ 1 (mod 3). The procedure is based on a method originally due to Voronoi that was recently adapted to purely cubic function fields of unit rank one. Our numerical examples show that the two fundamental units tend to have large degree, and frequently, the extension has a very small ideal class number.",

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KW - Minimum

KW - Purely cubic function field

KW - Reduced ideal

KW - Regulator

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Computation of the fundamental units and the regulator of a cyclic cubic function field

Abstract

Bibliographical note

Keywords

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