Truncated units. (English) Zbl 0759.11038

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)].


11R27 Units and factorization
Full Text: DOI


[1] Bernstein, L, (), Lecture Notes in Mathematics
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[5] Halter-Koch, F; Stender, H.-J; Halter-Koch, F; Stender, H.-J, Unabhängige einheiten für die Körper K = \(Q\)(\(D\^{}\{n\}±dn\)) mit dβdn, (), Abh. math. sem. univ. Hamburg, 50, 162-165, (1980), see also
[6] Sprindz̆uk, V.G, “almost every” algebraic number-field has a large class-number, Acta arith., 25, 411-413, (1974) · Zbl 0284.12003
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