Fundamentality of a cubic unit 𝑢 for ℤ[𝕦]

Beers, J.; Henshaw, D.; McCall, C.; Mulay, S.; Spindler, M.

doi:10.1090/S0025-5718-2010-02383-X

Fundamentality of a cubic unit $u$ for $\mathbb {Z}[u]$
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by J. Beers, D. Henshaw, C. K. McCall, S. B. Mulay and M. Spindler PDF

Math. Comp. 80 (2011), 563-578 Request permission

Corrigendum: Math. Comp. 81 (2012), 2383-2387.

Abstract:

Consider a cubic unit $u$ of positive discriminant. We present a computational proof of the fact that $u$ is a fundamental unit of the order $\mathbb {Z}[u]$ in most cases and determine the exceptions. This extends a similar (but restrictive) result due to E. Thomas.

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