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The unit rank classification of a cubic function field by its discriminant

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Abstract.

An arbitrary cubic function field can have 0, 1, or 2 for its unit rank. This paper presents the complete classification of unit rank of an arbitrary cubic function field by its discriminant and the polynomial discriminant of its generating polynomial. The notions of Kummer Theory and Cardano’s formula are used.

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Authors and Affiliations

  1. Department of Mathematics, Smith College, Northampton, MA, 01063, USA

    Y Lee

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  1. Y Lee
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Correspondence to Y Lee.

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Mathematics Subject Classification (2000): 11R27, 11R16

Acknowledgement The author expresses her gratitude to the referee for very helpful comments.

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Lee, Y. The unit rank classification of a cubic function field by its discriminant. manuscripta math. 116, 173–181 (2005). https://doi.org/10.1007/s00229-004-0530-5

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  • DOI: https://doi.org/10.1007/s00229-004-0530-5

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