A result of Schinzel. (Un résultat de Schinzel.) (French) Zbl 0802.11038

Summary: Let \(\alpha\neq 0,\pm 1\) be a totally real algebraic integer. A theorem of A. Schinzel [Corollary 1’ of Acta Arith. 26, 329-331 (1975; Zbl 0312.12001)] implies that the absolute height \(H(\alpha)\geq ({{1+ \sqrt{5}} \over 2})^{1/2}\). A very short proof of this result is given here.


11R04 Algebraic numbers; rings of algebraic integers
11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure


Zbl 0312.12001
Full Text: DOI Numdam EuDML


[1] Schinzel, A., Addendum to the paper “On the product of the conjugates outside the unit circle of an algebraic number” Acta Arith.24 (1973), 385-399, Acta Arith.26 (1975), 329-331. · Zbl 0312.12001
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