Truncated units. (English) Zbl 0759.11038

Levesque, Claude

J. Number Theory 41, No. 1, 48-68 (1992).

Let \(f=X^ n+k_ 1X^{n-1}+\cdots+k_{n-1}X+k_ n\in\mathbb{Z}[X]\) be irreducible, \(f(\omega)=0\), \(D\), \(d\in\mathbb{Z}\), \(D>0\), and \(\varepsilon=1+d^{-1}D\omega-d^{-1}\omega^ 2\). The author provides explicit criteria for \(\varepsilon\) to be an algebraic unit, and he produces tables of examples for \(n=4\) and \(n=6\). Special cases were previously settled by L. Bernstein [Math. Ann. 213, 275-279 (1975; Zbl 0284.12001)].

Reviewer: F.Halter-Koch (Graz)

MSC:

11R27

Units and factorization

Keywords:

algebraic unit; tables

Citations:

Zbl 0289.12006; Zbl 0284.12001

References:

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