Zentralblatt MATH

Publications of (and about) Paul Erdös
Zbl.No:  880.11067
Autor:  Erdös, Pál; Joó, I.; Schnitzer, F.J.
Title:  On Pisot numbers. (In English)
Source:  Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Math. 39, 95-99 (1996).
Review:  The algebraic integer 1 < q < 2 is called a Pisot number if |qi| < 1 for all of its conjugates. For a Pisot number q define the set Y by

Y = {sumi = 0n\epsiloniqi: n \geq 0, \epsiloni in Z, 0 \leq \epsiloni \leq 2}

and let

l2(q) = inf {|y1-y2|: y1,y2 in Y, y1\ne y2}.

The authors prove that if 1 < q < (1+\sqrt{5})/2, then q is a Pisot number if and only if l2(q) > 0.
Reviewer:  P.Kiss (Eger)
Classif.:  * 11R06 Special algebraic numbers
Keywords:  Pisot numbers; algebraic integers

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