Fundamental units for orders of unit rank 1 and generated by a unit

Abstract : Let ε be an algebraic unit for which the rank of the group of units of the order ℤ[ε] is equal to 1. Assume that ε is not a complex root of unity. It is natural to wonder whether ε is a fundamental unit of this order. It turns out that the answer is in general yes, and that a fundamental unit of this order can be explicitly given (as an explicit polynomial in ε) in the rare cases when the answer is no. This paper is a self-contained exposition of the solution to this problem, solution which was up to now scattered in many papers in the literature.
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Submitted on : Monday, March 14, 2016 - 3:42:08 PM
Last modification on : Monday, March 4, 2019 - 2:04:19 PM

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Stéphane R. Louboutin. Fundamental units for orders of unit rank 1 and generated by a unit. Banach Center Publications, Institute of Mathematics Polish Academy of Sciences, 2016, 108, pp.173 - 189. ⟨10.4064/bc108-0-14⟩. ⟨hal-01288083⟩

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