Approximation by polynomials with bounde
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Toufik Zaimi
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Article
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2007
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Elsevier Science
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English
β 177 KB
Let ΞΈ be a real number satisfying 1 < ΞΈ < 2, and let A(ΞΈ) be the set of polynomials with coefficients in {0, 1}, evaluated at ΞΈ . Using a result of Bugeaud, we prove by elementary methods that ΞΈ is a Pisot number when the set (A(ΞΈ) -A(ΞΈ) -A(ΞΈ)) is discrete; the problem whether Pisot numbers are the